Solve for x.

Question

$2\geqslant x-10\geqslant -12$
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:

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