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.