Algebra #2

Algebra Level 1

2 x − 3 5 + x + 3 4 = 4 x + 1 7 \frac{2x - 3}{5} + \frac{x + 3}{4} = \frac{4x + 1}{7}

Find the value of x . x.

− 112 -112 − 1 5 -\frac{1}{5} − 1 11 -\frac{1}{11} 0 0

Devansh Sangule by Devansh Sangule , 23, India

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2 solutions

Devansh Sangule
Sep 16, 2015

Solution:

⇒ 2 x − 3 5 + x + 3 4 = 4 x + 1 7 ⇒ 8 x − 12 20 + 5 x + 15 20 = 4 x + 1 7 ⇒ 8 x + 5 x − 12 + 15 20 = 4 x + 1 7 ⇒ 7 ( 8 x + 5 x − 12 + 15 ) = 20 ( 4 x + 1 ) ⇒ 56 x + 35 x − 84 + 105 = 80 x + 20 ⇒ 91 x + 21 = 80 x + 20 ⇒ 91 x − 80 x = 20 − 21 ⇒ 11 x = − 1 ⇒ x = − 1 11 \begin{aligned} &\Rightarrow \dfrac{ 2x - 3 }{ 5 } + \dfrac{ x + 3 }{ 4 } = \dfrac{ 4x + 1 }{ 7 }\\ &\Rightarrow \dfrac{ 8x - 12 }{ 20 } + \dfrac{ 5x + 15 }{ 20 } = \dfrac{ 4x + 1 }{ 7 }\\ &\Rightarrow \dfrac{ 8x + 5x - 12 + 15 }{ 20 } = \dfrac{ 4x + 1 }{ 7 }\\ &\Rightarrow 7 ( 8x + 5x - 12 + 15) = 20 ( 4x + 1)\\ &\Rightarrow 56x + 35x - 84 + 105 = 80x + 20\\ &\Rightarrow 91x + 21 = 80x + 20\\ &\Rightarrow 91x - 80x = 20 - 21\\ &\Rightarrow 11x = -1\\ &\Rightarrow \boxed {x = \dfrac{ -1 }{ 11 }}\\ \end{aligned}

8 Helpful 0 Interesting 0 Brilliant 1 Confused
Oon Han
Dec 9, 2018

Multiplying both sides by 140 gets rid of the fractions. 2 x − 3 5 + x + 3 4 = 4 x + 1 7 140 ( 2 x − 3 5 + x + 3 4 ) = 40 ( 4 x + 1 7 ) 56 x − 84 + 35 x + 105 = 80 x + 20 11 x = − 1 x = − 1 11 \begin{aligned} \frac{2x-3}{5}+\frac{x+3}{4} &= \frac{4x+1}{7} \\ 140\left(\frac{2x-3}{5}+\frac{x+3}{4}\right) &= 40\left(\frac{4x+1}{7}\right) \\ 56x-84+35x+105 &= 80x+20 \\ 11x &= -1 \\ x &= \boxed{-\frac{1}{11}} \end{aligned}

Therefore, the answer is − 1 11 \displaystyle -\frac{1}{11} .

0 Helpful 0 Interesting 0 Brilliant 1 Confused

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