To solve the equation [tex]\( |6y + 3| + 8 = 35 \)[/tex], follow these steps:
1. Isolate the absolute value:
[tex]\[
|6y + 3| + 8 = 35
\][/tex]
Subtract 8 from both sides:
[tex]\[
|6y + 3| = 35 - 8
\][/tex]
Simplify:
[tex]\[
|6y + 3| = 27
\][/tex]
2. Set up the two cases for the absolute value:
The expression inside the absolute value can be either 27 or -27. Therefore, we have two cases:
Case 1:
[tex]\[
6y + 3 = 27
\][/tex]
Case 2:
[tex]\[
6y + 3 = -27
\][/tex]
3. Solve for [tex]\( y \)[/tex] in each case:
Case 1:
[tex]\[
6y + 3 = 27
\][/tex]
Subtract 3 from both sides:
[tex]\[
6y = 24
\][/tex]
Divide by 6:
[tex]\[
y = \frac{24}{6}
\][/tex]
Simplify:
[tex]\[
y = 4
\][/tex]
Case 2:
[tex]\[
6y + 3 = -27
\][/tex]
Subtract 3 from both sides:
[tex]\[
6y = -30
\][/tex]
Divide by 6:
[tex]\[
y = \frac{-30}{6}
\][/tex]
Simplify:
[tex]\[
y = -5
\][/tex]
4. State the solutions:
The solutions to the equation [tex]\( |6y + 3| + 8 = 35 \)[/tex] are:
[tex]\[
y = 4 \quad \text{or} \quad y = -5
\][/tex]
So, the correct answer is [tex]\( y = 4 \)[/tex] or [tex]\( y = -5 \)[/tex].
