To solve the equation:
[tex]\[
|6y - 3| + 8 = 35
\][/tex]
First, isolate the absolute value expression by subtracting 8 from both sides:
[tex]\[
|6y - 3| + 8 - 8 = 35 - 8
\][/tex]
[tex]\[
|6y - 3| = 27
\][/tex]
Now, we need to solve the absolute value equation. Recall that if [tex]\(|A| = B\)[/tex], then [tex]\(A = B\)[/tex] or [tex]\(A = -B\)[/tex]. Applying this property here:
[tex]\[
6y - 3 = 27 \quad \text{or} \quad 6y - 3 = -27
\][/tex]
Let's solve each case separately.
### Case 1: [tex]\(6y - 3 = 27\)[/tex]
Add 3 to both sides:
[tex]\[
6y - 3 + 3 = 27 + 3
\][/tex]
[tex]\[
6y = 30
\][/tex]
Divide by 6:
[tex]\[
y = \frac{30}{6}
\][/tex]
[tex]\[
y = 5
\][/tex]
### Case 2: [tex]\(6y - 3 = -27\)[/tex]
Add 3 to both sides:
[tex]\[
6y - 3 + 3 = -27 + 3
\][/tex]
[tex]\[
6y = -24
\][/tex]
Divide by 6:
[tex]\[
y = \frac{-24}{6}
\][/tex]
[tex]\[
y = -4
\][/tex]
Therefore, the solutions for the equation [tex]\(|6y - 3| + 8 = 35\)[/tex] are:
[tex]\[
y = 5 \quad \text{or} \quad y = -4
\][/tex]
