Question

Solve the inequality.

–10 ≤ 2x – 4 < 8


–8 ≤ x < 2


–3 ≤ x < 2


–3 ≤ x < 6


–1 ≤ x < 8

Answer 1

To solve the compound inequality \(-10 ≤ 2x - 4 < 8\), we can break it down into two parts and solve each part separately.

1. Solve the first part:

\[
-10 ≤ 2x - 4
\]

Add 4 to both sides:

\[
-10 + 4 ≤ 2x
\]
\[
-6 ≤ 2x
\]

Now divide both sides by 2:

\[
-3 ≤ x
\]

2. Solve the second part:

\[
2x - 4 < 8
\]

Add 4 to both sides:

\[
2x < 8 + 4
\]

\[
2x < 12
\]

Now divide both sides by 2:

\[
x < 6
\]

Combining both parts, we have:

\[
-3 ≤ x < 6
\]

Thus, the solution to the inequality \(-10 ≤ 2x - 4 < 8\) is:

\[
[-3, 6)
\]

So the answer to choose from the provided options is:

\(-3 ≤ x < 6\)