1. ## Solving An Inequality

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

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

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:

$\displaystyle -5\leq\frac{1}{3}(x-4)\leq9$.......................... 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

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

And
$\displaystyle \frac{x-4}{3} \leq 9$
Your answer will be all thgose values of x which satisfies both
1st One

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

Multiply both sides by 3

$\displaystyle -15 \leq (x-4)$

$\displaystyle -11 \leq x$

2nd

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

Multily both sides by 3

$\displaystyle (x-4) \leq 27$

$\displaystyle x \leq 31$

$\displaystyle -11\leq x\leq 31$

$\displaystyle -5\leq\frac{1}{3}(x)-4\leq9$
1st Splitting
$\displaystyle -5 \leq \frac{x}{3}-4$

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

Multiply both sides by 3

$\displaystyle -3 \leq x$

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

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

Multiply both sides by 3

$\displaystyle x \leq 39$

$\displaystyle -3 \leq x\leq 39$