Question

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

Answer 1

To solve the inequality \( 5(-2 + x) < 3x + 2 \), first distribute the 5 on the left side:

\[
5(-2) + 5x < 3x + 2
\]
\[
-10 + 5x < 3x + 2
\]

Next, let's isolate the variable \( x \). Start by subtracting \( 3x \) from both sides:

\[
-10 + 5x - 3x < 2
\]
\[
-10 + 2x < 2
\]

Now, add 10 to both sides:

\[
2x < 2 + 10
\]
\[
2x < 12
\]

Finally, divide both sides by 2:

\[
x < 6
\]

Thus, the solution to the inequality is:

\[
\boxed{x < 6}
\]