# Thread: Solving An Inequality

1. ## Solving An Inequality

Hi, I'm having trouble with solving inequalities. Here's my question:

$-5\leq\frac{1}{3}x-4\leq9$

I'm not to sure on how to go about solving it... I know that you'll need to "split" the question into two, but other than that, I'm kind of stuck. Thanks!

2. Originally Posted by michaelleung
Hi, I'm having trouble with solving inequalities. Here's my question:

$-5\leq\frac{1}{3}(x-4)\leq9$.......................... IF THIS IS YOUR QUESTION

I'm not to sure on how to go about solving it... I know that you'll need to "split" the question into two, but other than that, I'm kind of stuck. Thanks!

Here's is splitting

$
-5 \leq \frac{x-4}{3}
$

And
$
\frac{x-4}{3} \leq 9

$

Your answer will be all thgose values of x which satisfies both
1st One

$
-5 \leq \frac{x-4}{3}
$

Multiply both sides by 3

$
-15 \leq (x-4)
$

Add 4 on both sides

$
-11 \leq x
$

2nd

$\frac{x-4}{3} \leq 9$

Multily both sides by 3

$
(x-4) \leq 27
$

Add 4 on both sides

$
x \leq 31
$

Hence your answer is

$
-11\leq x\leq 31
$

If your question is
$-5\leq\frac{1}{3}(x)-4\leq9$
1st Splitting
$
-5 \leq \frac{x}{3}-4
$

Add 4 on both sides

$-1 \leq \frac{x}{3}$

Multiply both sides by 3

$-3 \leq x$

2nd splitting
$\frac{1}{3}(x)-4\leq 9$

Add four on both sides

$\frac{1}{3} x \leq 13$

Multiply both sides by 3

$x \leq 39$

So your answer is

$-3 \leq x\leq 39$

3. Thanks for the reply! I really didn't understand, and I finally get it. Thanks again!