# How do you solve # 3 > 2|x-2|+5|x-2|#?

##### 1 Answer

Combine like terms; isolate the absolute value; solve for it; rewrite the inequality without the absolute value signs; isolate

#### Explanation:

Given:

#3>2abs(x-2)+5abs(x-2)#

**Step 1:** Since the value inside the absolute brackets is the same for both terms on the RHS, we can add them together:

#3>7abs(x-2)#

**Step 2:** We can now isolate the absolute value brackets by dividing both sides by 7, like this:

#3/7>abs(x-2)#

**Step 3:** When the absolute value of something (*smaller* than a specified value (*magnitude* must be less than that value. In this case, that means *must* be within

#–3/7" "<" "x-2" "<" "3/7#

**Step 4:** Isolate

#–3/7+2" "<" "x" "<" "3/7+2#

which reduces to

#11/7" "<" "x" "<" "17/7# .