Question

0.5 x minus 4 minus 2 x less than or equals 2

Answer 1

To solve the inequality \( 0.5x - 4 - 2x \leq 2 \), we can first combine like terms and isolate \( x \).

1. Combine the \( x \) terms:
\[
0.5x - 2x = -1.5x
\]
So the inequality becomes:
\[
-1.5x - 4 \leq 2
\]

2. Next, add 4 to both sides:
\[
-1.5x \leq 2 + 4
\]
\[
-1.5x \leq 6
\]

3. Now, divide both sides by -1.5. Remember, when we divide by a negative number, we must flip the inequality sign:
\[
x \geq \frac{6}{-1.5}
\]
\[
x \geq -4
\]

Thus, the solution to the inequality is:
\[
x \geq -4
\]