# How do you solve and graph #abs(-h+1.5)<3#?

##### 1 Answer

#### Answer:

$$1.5 < h < 4.5$$.

#### Explanation:

When you have an absolute value in an inequality you have to treat the two cases.

The first case is when the argument of the absolute value is positive $$-h+1.5\ge 0$$

that is when $$-h \ge -1.5$$

$$h\le1.5$$

and in this case you can simply remove the absolute value and treat it as a normal inequality

$$-h+1.5<3$$

$$-h<1.5$$

$$h>-1.5$$.

So when

$$-1.5 < h \le 1.5$$

The second case is when

$$-h+1.5< 0$$ or

$$h> 1.5$$

in this case the inequality is

$$-(-h+1.5)<3$$

$$h-1.5<3$$

$$h<4.5$$

that is

$$1.5 < h < 4.5$$.

Combining the two solutions (because the intervals overlaps in