Question

Which set expresses the solution to the compound inequality −2≤2x+13−4<1−2≤2x+13−4<1 ?(1 point)

Answer 1

Let's solve the compound inequality step by step:

The compound inequality given is:
\[
-2 \leq 2x + 13 - 4 < 1
\]

First, we can simplify the middle part:
\[
2x + 13 - 4 = 2x + 9
\]

So the compound inequality now looks like this:
\[
-2 \leq 2x + 9 < 1
\]

Now we can split this into two separate inequalities to solve them one at a time.

### 1. Solve \(-2 \leq 2x + 9\)

Subtract 9 from both sides:
\[
-2 - 9 \leq 2x
\]
\[
-11 \leq 2x
\]

Now, divide both sides by 2:
\[
-\frac{11}{2} \leq x
\]
or equivalently,
\[
x \geq -\frac{11}{2}
\]

### 2. Solve \(2x + 9 < 1\)

Subtract 9 from both sides:
\[
2x < 1 - 9
\]
\[
2x < -8
\]

Now, divide both sides by 2:
\[
x < -4
\]

### Combined Solution

The two parts of the compound inequality give us:
\[
-\frac{11}{2} \leq x < -4
\]

We can convert \(-\frac{11}{2}\) to a decimal to make it easier to see the ranges:
\(-\frac{11}{2} = -5.5\)

So, the combined solution is:
\[
-5.5 \leq x < -4
\]

In interval notation, this would be expressed as:
\[
[-5.5, -4)
\]

This interval represents the solution to the original compound inequality.