An algebra problem by A Former Brilliant Member

Algebra Level 2

Solve ∣ 2 x + 8 ∣ = 18 |2x+8| = 18 . Choose the most accurate option.

Notation: ∣ ⋅ ∣ | \cdot | denotes the absolute value function .

x = − 13 x = -13 x = 5 x = 5 x = − 13 , 5 x = -13 , 5 x = − 8 , 13 x = -8 , 13

A Former Brilliant Member by A Former Brilliant Member

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2 solutions

Tapas Mazumdar
Dec 24, 2016

∣ 2 x + 8 ∣ = 18 ⟹ ( 2 x + 8 ) 2 = 324 ⟹ 4 x 2 + 32 x + 64 = 324 ⟹ 4 x 2 + 32 x − 260 = 0 ⟹ x 2 + 8 x − 65 = 0 ⟹ x 2 + 13 x − 5 x − 65 = 0 ⟹ ( x + 13 ) ( x − 5 ) = 0 ⟹ x = − 13 or x = 5 \begin{aligned} & |2x+8| &=& 18 \\ \implies & {(2x+8)}^2 &=& 324 \\ \implies & 4x^2 + 32x + 64 &=& 324 \\ \implies & 4x^2 + 32x - 260 &=& 0 \\ \implies & x^2 + 8x - 65 &=& 0 \\ \implies & x^2 + 13x - 5x - 65 &=& 0 \\ \implies & (x+13)(x-5) &=& 0 \\ \implies & \boxed{x = -13} &\text{or}& \ \boxed{x = 5} \end{aligned}

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So 2x + 8= 18 or - 2x - 8=18. Solving gives x = - 13 or x = 8

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