Question

5(-2 + x) is less than 3x + 2

Answer 1

To solve the inequality \( 5(-2 + x) < 3x + 2 \), we can follow these steps:

1. Distribute the 5 on the left side:
\[
5(-2) + 5(x) < 3x + 2
\]
This simplifies to:
\[
-10 + 5x < 3x + 2
\]

2. Next, isolate the terms with \( x \) on one side and the constant terms on the other side. Subtract \( 3x \) from both sides:
\[
-10 + 5x - 3x < 2
\]
This simplifies to:
\[
-10 + 2x < 2
\]

3. Now, add 10 to both sides to isolate the term with \( x \):
\[
2x < 2 + 10
\]
This simplifies to:
\[
2x < 12
\]

4. Divide each side by 2 to solve for \( x \):
\[
x < 6
\]

Thus, the solution to the inequality \( 5(-2 + x) < 3x + 2 \) is:
\[
x < 6
\]