Question

10.
Solve the inequality.

14 + 10y ≥ 3(y + 14)

Answer 1

To solve the inequality \( 14 + 10y \geq 3(y + 14) \), we can start by distributing the \( 3 \) on the right side of the inequality:

\[
14 + 10y \geq 3y + 42
\]

Next, we will rearrange the inequality to get all terms involving \( y \) on one side and the constant terms on the other side. We can subtract \( 3y \) from both sides:

\[
14 + 10y - 3y \geq 42
\]

This simplifies to:

\[
14 + 7y \geq 42
\]

Now, we subtract \( 14 \) from both sides:

\[
7y \geq 42 - 14
\]
\[
7y \geq 28
\]

Next, we divide both sides by \( 7 \):

\[
y \geq 4
\]

Thus, the solution to the inequality is:

\[
\boxed{y \geq 4}
\]