# How do you solve (2x-9)/4<=x+2 and graph the solution on a number line?

Jul 13, 2017

$x \ge - \frac{17}{2}$

#### Explanation:

Multiply both sides by $4$:

$\frac{2 x - 9}{4} \le x + 2$

$4 \left(\frac{2 x - 9}{4}\right) \le 4 \left(x + 2\right)$

$2 x - 9 \le 4 x + 8$

Subtract $8$ from both sides.

$2 x - 9 - 8 \le 4 x + 8 - 8$

$2 x - 17 \le 4 x$

Next, subtract $2 x$ from both sides.

$2 x - 17 - 2 x \le 4 x - 2 x$

$- 17 \le 2 x$

Finally, divide both sides by 2.

$\frac{- 17}{2} \le \frac{2 x}{2}$

$- \frac{17}{2} \le x$

We can flip the inequality like this so it makes more sense:

$x \ge - \frac{17}{2}$

Notice that the sign still points towards the bigger number (x). This inequality means that $x$ is greater than $- \frac{17}{2}$, so to graph it on a number line, we will draw a solid dot on $- \frac{17}{2}$ to indicate that $x$ could be that number, and then shade in everything to the right of $- \frac{17}{2}$, since $x$ can also be anything greater than it.