Question

Solve the inequalities.
-3 /geq x + 2 /geq /4

Answer 1

To solve the compound inequality \(-3 \geq x + 2 \geq 4\), we can break it down into two separate inequalities:

1. \(-3 \geq x + 2\)
2. \(x + 2 \geq 4\)

### Step 1: Solve the first inequality \(-3 \geq x + 2\)

Subtract \(2\) from both sides:

\[
-3 - 2 \geq x
\]
\[
-5 \geq x
\]
or equivalently,

\[
x \leq -5
\]

### Step 2: Solve the second inequality \(x + 2 \geq 4\)

Subtract \(2\) from both sides:

\[
x \geq 4 - 2
\]
\[
x \geq 2
\]

### Final Step: Combine the results

We now have the two inequalities:

1. \(x \leq -5\)
2. \(x \geq 2\)

There is no value of \(x\) that can satisfy both inequalities at the same time (as \(-5\) is less than \(2\)), so there is no solution.

### Conclusion
The compound inequality \(-3 \geq x + 2 \geq 4\) has no solution.