∣ a x − 17 ∣ ≤ b \lvert ax-17 \rvert \leq b

Algebra Level 2

If a b < 0 ab<0 , the solution to the inequality ∣ a x − 17 ∣ ≤ b \lvert ax-17 \rvert \leq b is − 7 ≤ x ≤ 5. -7 \leq x \leq 5. What is the value of a + b ? a+b?

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Mahindra Jain by Mahindra Jain

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4 solutions

Raj Dave
Mar 19, 2014

Question is wrong. ab can't be negative. a=-17 , b=-102 gives the solution.

1 Helpful 0 Interesting 0 Brilliant 1 Confused

i got it right 85, but my little brother disturb me and make me click on C answer,, -_-

Yodji Fufuri - 7 years, 2 months ago
Nikhil Kashyap
Mar 16, 2014

Take two cases

Case A: a>0, b<0

Case B: a<0, b>0

1 Helpful 0 Interesting 0 Brilliant 1 Confused
Aris M
Mar 16, 2020

For all those saying that b b could be negative, no it couldn't. Here's why:

The absolute value of anything can never be negative. Therefore, ∣ a x − 17 ∣ ≥ 0 ∣ax-17∣\geq 0 . If b ≤ 0 b \leq 0 then the inequality would have no solutions, since something nonnegative could never be less than or equal to something negative. This is contradictory to the information provided, since we know that the inequality has a solution, specifically − 7 ≤ x ≤ 5 -7≤x≤5 . Therefore b b must be positive, and a a must be negative. Note that a ≠ 0 a \neq 0 and b ≠ 0 b \neq 0 . If either one was equal to 0 0 , then the condition a b < 0 ab < 0 would not be satisfied.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Mas Mus
Apr 13, 2014

a 2 x 2 − 34 a x + 289 = b 2 . . . . ( 1 ) \ % M a t h T y p e ! M T E F ! 2 ! 1 ! + − % f e a a g K a r t 1 e v 2 a a a t C v A U f e B S j u y Z L 2 y d 9 g z L b v y N v 2 C a e r b u L w B L n % h i o v 2 D G i 1 B T f M B a e X a t L x B I 9 g B a e r b d 9 w D Y L w z Y b I t L D h a r q q t u b s r % 4 r N C H b G e a G q i V u 0 J e 9 s q q r p e p C 0 x b b L 8 F 4 r q q r F f p e e a 0 x e 9 L q − J c 9 % v q a q p e p m 0 x b b a 9 p w e 9 Q 8 f s 0 − y q a q p e p a e 9 p g 0 F i r p e p e K k F r 0 x f r − x % f r − x b 9 a d b a q a a e G a c i G a a i a a b e q a a m a a b a a b a a G c b a G a a m y y a m a a C a % a a l e q a b a G a a G O m a a a a k i a a d I h a d a a h a a W c b e q a a i a a i k d a a a G c c q G H % s i s l c a a I Z a G a a G i n a i a a d g g a c a W G 4 b G a e y 4 k a S I a a G O m a i a a i I d a c a % a I 5 a G a e y y p a 0 J a a m O y a m a a C a a a l e q a b a G a a G O m a a a a a a a ! 4403 ! {a^2}{x^2} - 34ax + 289 = {b^2}....(1)\ \% MathType!MTEF!2!1!+- \% feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn \% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr \% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 \% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x \% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyyamaaCa \% aaleqabaGaaGOmaaaakiaadIhadaahaaWcbeqaaiaaikdaaaGccqGH \% sislcaaIZaGaaGinaiaadggacaWG4bGaey4kaSIaaGOmaiaaiIdaca \% aI5aGaeyypa0JaamOyamaaCaaaleqabaGaaGOmaaaaaaa!4403! S u b t i t u s i o n x = − 7 a n d x = 5 % M a t h T y p e ! M T E F ! 2 ! 1 ! + − % f e a a g K a r t 1 e v 2 a a a t C v A U f e B S j u y Z L 2 y d 9 g z L b v y N v 2 C a e r b u L w B L n % h i o v 2 D G i 1 B T f M B a e X a t L x B I 9 g B a e r b d 9 w D Y L w z Y b I t L D h a r q q t u b s r % 4 r N C H b G e a G q i V u 0 J e 9 s q q r p e p C 0 x b b L 8 F 4 r q q r F f p e e a 0 x e 9 L q − J c 9 % v q a q p e p m 0 x b b a 9 p w e 9 Q 8 f s 0 − y q a q p e p a e 9 p g 0 F i r p e p e K k F r 0 x f r − x % f r − x b 9 a d b a q a a e G a c i G a a i a a b e q a a m a a b a a b a a G c b a G a a e 4 u a i a a b w % h a c a q G I b G a a e i D a i a a b M g a c a q G 0 b G a a e y D a i a a b o h a c a q G P b G a a e 4 B % a i a a b 6 g a c a a M e 8 U a a m i E a i a b g 2 d a 9 i a b g k H i T i a a i E d a c a a M e 8 U a a e % y y a i a a b 6 g a c a q G K b G a a G j b V l a a d I h a c q G H 9 a q p c a a I 1 a a a a a ! 4 E 16 ! {\rm{Subtitusion}}\;x = - 7\;{\rm{and}}\;x = 5 \% MathType!MTEF!2!1!+- \% feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn \% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr \% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 \% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x \% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaae4uaiaabw \% hacaqGIbGaaeiDaiaabMgacaqG0bGaaeyDaiaabohacaqGPbGaae4B \% aiaab6gacaaMe8UaamiEaiabg2da9iabgkHiTiaaiEdacaaMe8Uaae \% yyaiaab6gacaqGKbGaaGjbVlaadIhacqGH9aqpcaaI1aaaaa!4E16! 49 a 2 + 238 a + 289 = b 2 . . . . ( 2 ) 25 a 2 − 170 a + 289 = b 2 . . . . . ( 3 ) % M a t h T y p e ! M T E F ! 2 ! 1 ! + − % f e a a g K a r t 1 e v 2 a a a t C v A U f e B S j u y Z L 2 y d 9 g z L b v y N v 2 C a e r b u L w B L n % h i o v 2 D G i 1 B T f M B a e X a t L x B I 9 g B a e r b d 9 w D Y L w z Y b I t L D h a r q q t u b s r % 4 r N C H b G e a G q i V u 0 J e 9 s q q r p e p C 0 x b b L 8 F 4 r q q r F f p e e a 0 x e 9 L q − J c 9 % v q a q p e p m 0 x b b a 9 p w e 9 Q 8 f s 0 − y q a q p e p a e 9 p g 0 F i r p e p e K k F r 0 x f r − x % f r − x b 9 a d b a q a a e G a c i G a a i a a b e q a a m a a b a a b a a G c e a q a b e a a c a a I 0 a % G a a G y o a i a a d g g a d a a h a a W c b e q a a i a a i k d a a a G c c q G H R a W k c a a I Y a G a % a G 4 m a i a a i I d a c a W G H b G a e y 4 k a S I a a G O m a i a a i I d a c a a I 5 a G a e y y p a 0 % J a a m O y a m a a C a a a l e q a b a G a a G O m a a a a k i a a c 6 c a c a G G U a G a a i O l a i a a % c 6 c a c a G G O a G a a G y m a i a a c M c a a e a a c a a I Y a G a a G y n a i a a d g g a d a a h a a % W c b e q a a i a a i k d a a a G c c q G H s i s l c a a I X a G a a G 4 n a i a a i c d a c a W G H b G a % e y 4 k a S I a a G O m a i a a i I d a c a a I 5 a G a e y y p a 0 J a a m O y a m a a C a a a l e q a b a % G a a G O m a a a a k i a a c 6 c a c a G G U a G a a i O l a i a a c 6 c a c a G G U a G a a i i k a i a a % i k d a c a G G P a a a a a a ! 5 B 28 ! \begin{array}{l}49{a^2} + 238a + 289 = {b^2}....(2)\\25{a^2} - 170a + 289 = {b^2}.....(3)\end{array} \% MathType!MTEF!2!1!+- \% feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn \% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr \% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 \% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x \% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaaI0a \% GaaGyoaiaadggadaahaaWcbeqaaiaaikdaaaGccqGHRaWkcaaIYaGa \% aG4maiaaiIdacaWGHbGaey4kaSIaaGOmaiaaiIdacaaI5aGaeyypa0 \% JaamOyamaaCaaaleqabaGaaGOmaaaakiaac6cacaGGUaGaaiOlaiaa \% c6cacaGGOaGaaGymaiaacMcaaeaacaaIYaGaaGynaiaadggadaahaa \% WcbeqaaiaaikdaaaGccqGHsislcaaIXaGaaG4naiaaicdacaWGHbGa \% ey4kaSIaaGOmaiaaiIdacaaI5aGaeyypa0JaamOyamaaCaaaleqaba \% GaaGOmaaaakiaac6cacaGGUaGaaiOlaiaac6cacaGGUaGaaiikaiaa \% ikdacaGGPaaaaaa!5B28! S u b t r u c t ( 2 ) b y ( 3 ) a n d s i m p l p y i t t o g e t a % M a t h T y p e ! M T E F ! 2 ! 1 ! + − % f e a a g K a r t 1 e v 2 a a a t C v A U f e B S j u y Z L 2 y d 9 g z L b v y N v 2 C a e r b u L w B L n % h i o v 2 D G i 1 B T f M B a e X a t L x B I 9 g B a e r b d 9 w D Y L w z Y b I t L D h a r q q t u b s r % 4 r N C H b G e a G q i V u 0 J e 9 s q q r p e p C 0 x b b L 8 F 4 r q q r F f p e e a 0 x e 9 L q − J c 9 % v q a q p e p m 0 x b b a 9 p w e 9 Q 8 f s 0 − y q a q p e p a e 9 p g 0 F i r p e p e K k F r 0 x f r − x % f r − x b 9 a d b a q a a e G a c i G a a i a a b e q a a m a a b a a b a a G c b a G a a e 4 u a i a a b w % h a c a q G I b G a a e i D a i a a b k h a c a q G 1 b G a a e 4 y a i a a b s h a c a a M e 8 U a a e i k % a i a a b k d a c a q G P a G a a G j b V l a a b k g a c a q G 5 b G a a G j b V l a a b I c a c a q G Z a % G a a e y k a i a a y s W 7 c a q G H b G a a e O B a i a a b s g a c a a M e 8 U a a e 4 C a i a a b M g a % c a q G T b G a a e i C a i a a b Y g a c a q G W b G a a e y E a i a a y s W 7 c a q G P b G a a e i D a i % a a y s W 7 c a q G 0 b G a a e 4 B a i a a y s W 7 c a q G N b G a a e y z a i a a b s h a c a a M e 8 U a % a m y y a a a a ! 6233 ! {\rm{Subtruct}}\;{\rm{(2)}}\;{\rm{by}}\;{\rm{(3)}}\;{\rm{and}}\;{\rm{simplpy}}\;{\rm{it}}\;{\rm{to}}\;{\rm{get}}\;a \% MathType!MTEF!2!1!+- \% feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn \% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr \% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 \% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x \% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaae4uaiaabw \% hacaqGIbGaaeiDaiaabkhacaqG1bGaae4yaiaabshacaaMe8Uaaeik \% aiaabkdacaqGPaGaaGjbVlaabkgacaqG5bGaaGjbVlaabIcacaqGZa \% GaaeykaiaaysW7caqGHbGaaeOBaiaabsgacaaMe8Uaae4CaiaabMga \% caqGTbGaaeiCaiaabYgacaqGWbGaaeyEaiaaysW7caqGPbGaaeiDai \% aaysW7caqG0bGaae4BaiaaysW7caqGNbGaaeyzaiaabshacaaMe8Ua \% amyyaaaa!6233! a ( a + 17 ) = 0 a = 0 , a = − 17 % M a t h T y p e ! M T E F ! 2 ! 1 ! + − % f e a a g K a r t 1 e v 2 a a a t C v A U f e B S j u y Z L 2 y d 9 g z L b v y N v 2 C a e r b u L w B L n % h i o v 2 D G i 1 B T f M B a e X a t L x B I 9 g B a e r b d 9 w D Y L w z Y b I t L D h a r q q t u b s r % 4 r N C H b G e a G q i V u 0 J e 9 s q q r p e p C 0 x b b L 8 F 4 r q q r F f p e e a 0 x e 9 L q − J c 9 % v q a q p e p m 0 x b b a 9 p w e 9 Q 8 f s 0 − y q a q p e p a e 9 p g 0 F i r p e p e K k F r 0 x f r − x % f r − x b 9 a d b a q a a e G a c i G a a i a a b e q a a m a a b a a b a a G c e a q a b e a a c a W G H b % G a a i i k a i a a d g g a c q G H R a W k c a a I X a G a a G 4 n a i a a c M c a c q G H 9 a q p c a a I % W a a a b a G a a m y y a i a b g 2 d a 9 i a a i c d a c a G G S a G a a G z b V l a a d g g a c q G H 9 a % q p c q G H s i s l c a a I X a G a a G 4 n a a a a a a ! 4679 ! \begin{array}{l}a(a + 17) = 0\\a = 0,\quad a = - 17\end{array} \% MathType!MTEF!2!1!+- \% feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn \% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr \% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 \% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x \% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWGHb \% GaaiikaiaadggacqGHRaWkcaaIXaGaaG4naiaacMcacqGH9aqpcaaI \% WaaabaGaamyyaiabg2da9iaaicdacaGGSaGaaGzbVlaadggacqGH9a \% qpcqGHsislcaaIXaGaaG4naaaaaa!4679! W e k n o w t h a t a b < 0 t h e n a = 0 i s n o t a s o l u t i o n . F i n d t h e v a l u e o f b b y c h a n g i n g a = − 17 t o ( 2 ) . W e w i l l f i n d b = − 102 a n d b = 102. S i n c e a b < 0 a n d a = − 7 , t h e n b = 102. H e n c e , a + b = 85. % M a t h T y p e ! M T E F ! 2 ! 1 ! + − % f e a a g K a r t 1 e v 2 a a a t C v A U f e B S j u y Z L 2 y d 9 g z L b v y N v 2 C a e r b u L w B L n % h i o v 2 D G i 1 B T f M B a e X a t L x B I 9 g B a e r b d 9 w D Y L w z Y b I t L D h a r q q t u b s r % 4 r N C H b G e a G q i V u 0 J e 9 s q q r p e p C 0 x b b L 8 F 4 r q q r F f p e e a 0 x e 9 L q − J c 9 % v q a q p e p m 0 x b b a 9 p w e 9 Q 8 f s 0 − y q a q p e p a e 9 p g 0 F i r p e p e K k F r 0 x f r − x % f r − x b 9 a d b a q a a e G a c i G a a i a a b e q a a m a a b a a b a a G c e a q a b e a a c a q G x b % G a a e y z a i a a y k W 7 c a q G R b G a a e O B a i a a b + g a c a q G 3 b G a a G P a V l a a b s h a % c a q G O b G a a e y y a i a a b s h a c a a M c 8 U a a m y y a i a a d k g a c q G H 8 a a p c a a I W a % G a a G P a V l a a b s h a c a q G O b G a a e y z a i a a b 6 g a c a a M c 8 U a a m y y a i a b g 2 d a % 9 i a a i c d a c a a M c 8 U a a e y A a i a a b o h a c a a M c 8 U a a e O B a i a a b + g a c a q G 0 b % G a a G P a V l a a b g g a c a a M c 8 U a a e 4 C a i a a b + g a c a q G S b G a a e y D a i a a b s h a % c a q G P b G a a e 4 B a i a a b 6 g a c a q G U a G a a G P a V l a a b A e a c a q G P b G a a e O B a i % a a b s g a c a a M c 8 U a a e i D a i a a b I g a c a q G L b G a a G P a V l a a b A h a c a q G H b G a % a e i B a i a a b w h a c a q G L b G a a e i i a i a a y k W 7 c a q G V b G a a e O z a i a a b c c a c a % a M c 8 U a a m O y a i a a b c c a c a a M c 8 U a a e O y a i a a b M h a c a q G G a G a a G P a V l a a % b o g a c a q G O b G a a e y y a i a a b 6 g a c a q G N b G a a e y A a i a a b 6 g a c a q G N b G a a e % i i a i a a y k W 7 c a W G H b G a e y y p a 0 J a e y O e I 0 I a a G y m a i a a i E d a c a q G G a G a % a G P a V l a a b s h a c a q G V b G a a e i i a i a a y k W 7 c a q G O a G a a e O m a i a a b M c a c a % q G U a a a b a G a a e 4 v a i a a b w g a c a q G G a G a a G P a V l a a b E h a c a q G P b G a a e i B % a i a a b Y g a c a q G G a G a a G P a V l a a b A g a c a q G P b G a a e O B a i a a b s g a c a q G G a % G a a G P a V l a a d k g a c q G H 9 a q p c q G H s i s l c a a I X a G a a G i m a i a a i k d a c a q G % G a G a a G P a V l a a b g g a c a q G U b G a a e i z a i a a b c c a c a a M c 8 U a a m O y a i a b g 2 % d a 9 i a a i g d a c a a I W a G a a G O m a i a a b 6 c a c a q G G a G a a G P a V l a a b o f a c a q G % P b G a a e O B a i a a b o g a c a q G L b G a a e i i a i a a y k W 7 c a W G H b G a a m O y a i a b g Y % d a 8 i a a i c d a c a q G G a G a a G P a V l a a b g g a c a q G U b G a a e i z a i a a b c c a c a a M % c 8 U a a m y y a i a b g 2 d a 9 i a b g k H i T i a a i E d a c a q G S a G a a e i i a i a a y k W 7 c a % q G 0 b G a a e i A a i a a b w g a c a q G U b G a a e i i a i a a y k W 7 c a W G I b G a e y y p a 0 J a % a G y m a i a a i c d a c a a I Y a G a a e O l a i a a b c c a c a a M c 8 U a a e i s a i a a b w g a c a % q G U b G a a e 4 y a i a a b w g a c a q G S a G a a e i i a i a a y k W 7 c a W G H b G a e y 4 k a S I a % a m O y a i a b g 2 d a 9 i a a i I d a c a a I 1 a G a a i O l a a a a a a ! E D 9 A ! \begin{array}{l}{\rm{We}}\,{\rm{know}}\,{\rm{that}}\,ab < 0\,{\rm{then}}\,a = 0\,{\rm{is}}\,{\rm{not}}\,{\rm{a}}\,{\rm{solution}}{\rm{.}}\,{\rm{Find}}\,{\rm{the}}\,{\rm{value }}\,{\rm{of }}\,b{\rm{ }}\,{\rm{by }}\,{\rm{changing }}\,a = - 17{\rm{ }}\,{\rm{to }}\,{\rm{(2)}}{\rm{.}}\\{\rm{We }}\,{\rm{will }}\,{\rm{find }}\,b = - 102{\rm{ }}\,{\rm{and }}\,b = 102.{\rm{ }}\,{\rm{Since }}\,ab < 0{\rm{ }}\,{\rm{and }}\,a = - 7{\rm{, }}\,{\rm{then }}\,b = 102.{\rm{ }}\,{\rm{Hence, }}\,a + b = 85.\end{array} \% MathType!MTEF!2!1!+- \% feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn \% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr \% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 \% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x \% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaqGxb \% GaaeyzaiaaykW7caqGRbGaaeOBaiaab+gacaqG3bGaaGPaVlaabsha \% caqGObGaaeyyaiaabshacaaMc8UaamyyaiaadkgacqGH8aapcaaIWa \% GaaGPaVlaabshacaqGObGaaeyzaiaab6gacaaMc8Uaamyyaiabg2da \% 9iaaicdacaaMc8UaaeyAaiaabohacaaMc8UaaeOBaiaab+gacaqG0b \% GaaGPaVlaabggacaaMc8Uaae4Caiaab+gacaqGSbGaaeyDaiaabsha \% caqGPbGaae4Baiaab6gacaqGUaGaaGPaVlaabAeacaqGPbGaaeOBai \% aabsgacaaMc8UaaeiDaiaabIgacaqGLbGaaGPaVlaabAhacaqGHbGa \% aeiBaiaabwhacaqGLbGaaeiiaiaaykW7caqGVbGaaeOzaiaabccaca \% aMc8UaamOyaiaabccacaaMc8UaaeOyaiaabMhacaqGGaGaaGPaVlaa \% bogacaqGObGaaeyyaiaab6gacaqGNbGaaeyAaiaab6gacaqGNbGaae \% iiaiaaykW7caWGHbGaeyypa0JaeyOeI0IaaGymaiaaiEdacaqGGaGa \% aGPaVlaabshacaqGVbGaaeiiaiaaykW7caqGOaGaaeOmaiaabMcaca \% qGUaaabaGaae4vaiaabwgacaqGGaGaaGPaVlaabEhacaqGPbGaaeiB \% aiaabYgacaqGGaGaaGPaVlaabAgacaqGPbGaaeOBaiaabsgacaqGGa \% GaaGPaVlaadkgacqGH9aqpcqGHsislcaaIXaGaaGimaiaaikdacaqG \% GaGaaGPaVlaabggacaqGUbGaaeizaiaabccacaaMc8UaamOyaiabg2 \% da9iaaigdacaaIWaGaaGOmaiaab6cacaqGGaGaaGPaVlaabofacaqG \% PbGaaeOBaiaabogacaqGLbGaaeiiaiaaykW7caWGHbGaamOyaiabgY \% da8iaaicdacaqGGaGaaGPaVlaabggacaqGUbGaaeizaiaabccacaaM \% c8Uaamyyaiabg2da9iabgkHiTiaaiEdacaqGSaGaaeiiaiaaykW7ca \% qG0bGaaeiAaiaabwgacaqGUbGaaeiiaiaaykW7caWGIbGaeyypa0Ja \% aGymaiaaicdacaaIYaGaaeOlaiaabccacaaMc8Uaaeisaiaabwgaca \% qGUbGaae4yaiaabwgacaqGSaGaaeiiaiaaykW7caWGHbGaey4kaSIa \% amOyaiabg2da9iaaiIdacaaI1aGaaiOlaaaaaa!ED9A!

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