College

Solve the absolute value equation:

[tex]2|4x-5|-8=-6[/tex]

A. [tex]x = \frac{3}{2}[/tex] or [tex]x = 1[/tex]
B. [tex]x = \frac{7}{8}[/tex] or [tex]x = 1[/tex]
C. [tex]x = \frac{7}{8}[/tex] or [tex]x = \frac{19}{8}[/tex]
D. [tex]x = \frac{7}{8}[/tex] or [tex]x = \frac{3}{2}[/tex]

Answer :

Let's solve the equation [tex]\(2|4x - 5| - 8 = -6\)[/tex] step by step.

Step 1: Simplify the equation.

First, add 8 to both sides to isolate the absolute value term:
[tex]\[
2|4x - 5| = 2
\][/tex]

Step 2: Divide both sides by 2 to further simplify:
[tex]\[
|4x - 5| = 1
\][/tex]

Step 3: Set up two separate equations to solve for [tex]\(x\)[/tex], since the expression inside the absolute value can be either positive or negative.

- Equation 1: [tex]\(4x - 5 = 1\)[/tex]

Solve for [tex]\(x\)[/tex]:
[tex]\[
4x - 5 = 1
\][/tex]
Add 5 to both sides:
[tex]\[
4x = 6
\][/tex]
Divide by 4:
[tex]\[
x = \frac{6}{4} = \frac{3}{2}
\][/tex]

- Equation 2: [tex]\(4x - 5 = -1\)[/tex]

Solve for [tex]\(x\)[/tex]:
[tex]\[
4x - 5 = -1
\][/tex]
Add 5 to both sides:
[tex]\[
4x = 4
\][/tex]
Divide by 4:
[tex]\[
x = 1
\][/tex]

Step 4: Conclusion.

The possible solutions for the given equation are [tex]\(x = \frac{3}{2}\)[/tex] and [tex]\(x = 1\)[/tex].

So, the correct answer is A. [tex]\(x = \frac{3}{2}\)[/tex] or [tex]\(x = 1\)[/tex].

Other Questions