Verified Answer :

W0lf93

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.

johanrusli

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

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