Question

3(x+4) is greater than or equal to 2x + 5

Answer 1

To solve the inequality \( 3(x + 4) \geq 2x + 5 \), follow these steps:

1. Distribute the 3 on the left side:
\[
3x + 12 \geq 2x + 5
\]

2. Subtract \( 2x \) from both sides to get all the \( x \) terms on one side:
\[
3x - 2x + 12 \geq 5
\]
Simplifying this, we have:
\[
x + 12 \geq 5
\]

3. Subtract 12 from both sides to isolate \( x \):
\[
x \geq 5 - 12
\]
Simplifying gives:
\[
x \geq -7
\]

Thus, the solution to the inequality \( 3(x + 4) \geq 2x + 5 \) is:
\[
\boxed{x \geq -7}
\]