Question

-7 os less than or equal to 2x + 1 < 11

Answer 1

To solve the compound inequality \(-7 \leq 2x + 1 < 11\), we can break it into two parts and solve each part separately.

1. Solve the left part: \(-7 \leq 2x + 1\)

Subtract 1 from both sides:
\[
-7 - 1 \leq 2x
\]
\[
-8 \leq 2x
\]

Now, divide by 2:
\[
-4 \leq x \quad \text{or} \quad x \geq -4
\]

2. Solve the right part: \(2x + 1 < 11\)

Subtract 1 from both sides:
\[
2x < 11 - 1
\]
\[
2x < 10
\]

Now, divide by 2:
\[
x < 5
\]

Now we combine the two results:
\[
-4 \leq x < 5
\]

So the solution to the compound inequality \(-7 \leq 2x + 1 < 11\) is:
\[
[-4, 5)
\]