Question

Solve for x.
$2\geqslant x-10\geqslant -12$
Write your answer as a compound inequality with integers.
$12\gt x\geqslant -2$
$x\geqslant 12$ or $x\leqslant -2$
$12\geqslant x\geqslant -2$
$x\gt 12$ or $x\leqslant -2$

Answer 1

To solve the compound inequality \(2 \geqslant x - 10 \geqslant -12\), we will break it down into two parts:

1. \(2 \geqslant x - 10\)
2. \(x - 10 \geqslant -12\)

Starting with the first part:

\[
2 \geqslant x - 10
\]

Adding \(10\) to both sides gives:

\[
2 + 10 \geqslant x
\]

\[
12 \geqslant x
\]

This can be rewritten as:

\[
x \leqslant 12
\]

Now, let's solve the second part:

\[
x - 10 \geqslant -12
\]

Adding \(10\) to both sides gives:

\[
x \geqslant -12 + 10
\]

\[
x \geqslant -2
\]

Now combining both results, we have:

\[
-2 \leqslant x \leqslant 12
\]

Rewriting this in the standard form of a compound inequality gives:

\[
12 \geqslant x \geqslant -2
\]

Thus, the final answer is:

\[
\boxed{12 \geqslant x \geqslant -2}
\]