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Solve the equation. If there is more than one solution, separate them with a comma.

[tex]\[ |6x - 4| = 8 \][/tex]

[tex]\(\square\)[/tex]

Sagot :

GinnyAnswer
To solve the equation [tex]\(|6x - 4| = 8\)[/tex], we must consider the nature of absolute value. The absolute value equation [tex]\( |A| = B \)[/tex] implies that [tex]\( A = B \)[/tex] or [tex]\( A = -B \)[/tex]. Applying this to our problem, we set up two separate equations:

### Case 1: [tex]\( 6x - 4 = 8 \)[/tex]

1. Solve for [tex]\( x \)[/tex]:
[tex]\[ 6x - 4 = 8 \][/tex]

2. Add 4 to both sides:
[tex]\[ 6x = 12 \][/tex]

3. Divide both sides by 6:
[tex]\[ x = \frac{12}{6} \][/tex]

4. Simplify the division:
[tex]\[ x = 2 \][/tex]

### Case 2: [tex]\( 6x - 4 = -8 \)[/tex]

1. Solve for [tex]\( x \)[/tex]:
[tex]\[ 6x - 4 = -8 \][/tex]

2. Add 4 to both sides:
[tex]\[ 6x = -4 \][/tex]

3. Divide both sides by 6:
[tex]\[ x = \frac{-4}{6} \][/tex]

4. Simplify the division:
[tex]\[ x = -\frac{2}{3} \][/tex]

Therefore, the solutions to the equation [tex]\(|6x - 4| = 8\)[/tex] are [tex]\( x = 2 \)[/tex] and [tex]\( x = -\frac{2}{3} \)[/tex]. In comma-separated form, the answers are:
[tex]\[ x = 2, -\frac{2}{3} \][/tex]
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