Question

Solve the equation. Check for extraneous solutions.

9|9 – 8x| = 2x + 3

Answer 1

The given equation is : 9|9-8x| = 2x + 3. Removing the modulus sign to get, 9(9-8x) = +2x+3 or 9(9-8x) = -2x-3 . Case 1: 9(9-8x) = +2x+3 or 81 -72x = 2x +3 or 78 = 74x or x = 78/74. Case 2:9(9-8x) = -2x-3 or 81 - 72x =- 2x -3 or 70x = 84 or x = 84/70. Thus, the solutions of x are 78/74 and 84/70. No, these are not extraneous solutions, as the answers are satisfying the equation.

Answer 2

The solution of 9|9 – 8x| = 2x + 3 is 39/37 or 6/5

Further explanation

We need to recall the following definitions to solve absolute equation.

$| x - a | = \sqrt { (x - a)^2 }$

If | x | > a then x > a or x < -a

If | x | < a then -a < x < a

Let us tackle the problem.

This problem is about linear absolute equation.

Given:

$9 | 9 - 8x | = 2x + 3$

If x ≤ 9/8 , then :

$9 ( 9 - 8x ) = 2x + 3$

$81 - 72x = 2x + 3$

$81 - 3 = 72x + 2x$

$78 = 74x$

$x = 78 / 74$

$x = \boxed {\frac{39}{37}}$

If x > 9/8 , then :

$-9 ( 9 - 8x ) = 2x + 3$

$-81 + 72x = 2x + 3$

$-81 - 3 = -72x + 2x$

$-84 = -70x$

$x = -84 / -70$

$x = \boxed {\frac{6}{5}}$

Learn more

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Answer details

Grade: High School

Subject: Mathematics

Chapter: Absolute Equations

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Absolute