To solve the equation [tex]\(71y = 14(5y + 29)\)[/tex], follow these steps:
1. Distribute the 14 on the right side of the equation:
[tex]\[
14(5y + 29) = 14 \cdot 5y + 14 \cdot 29
\][/tex]
Simplify:
[tex]\[
14 \cdot 5y = 70y
\][/tex]
[tex]\[
14 \cdot 29 = 406
\][/tex]
So,
[tex]\[
14(5y + 29) = 70y + 406
\][/tex]
2. Now, set the left side equal to the right side:
[tex]\[
71y = 70y + 406
\][/tex]
3. Subtract [tex]\(70y\)[/tex] from both sides to isolate [tex]\(y\)[/tex]:
[tex]\[
71y - 70y = 406
\][/tex]
Simplify the left side:
[tex]\[
y = 406
\][/tex]
The value of [tex]\(y\)[/tex] that satisfies the equation is:
[tex]\[
y = 406
\][/tex]
