Question

What are the solutions to the equation |2x-3|+4=17

Answer 1

`|2x-3|=\left\{\begin{array}{ccc}2x-3&for&2x-3\geq0\to x\geq1.5\\-(2x-3)&for&2x-3 < 0\to x<1.5\end{array}\right\\.\\\\(1)\qquad x < 1.5\to|2x-3|=-(2x-3)=3-2x\\\\3-2x+4=17\\7-2x=17\ \ \ |-7\\-2x=10\ \ \ \ |:(-2)\\x=-5\\\\(2)\qquad x\geq1.5\to|2x-3|=2x-3\\\\2x-3+4=17\\2x+1=17\ \ \ |-1\\2x=16\ \ \ |:2\\x=8\geq1.5\\\\Answer:\ x=-5\ \vee\ x=8`

Answer 2

First, let's subtract both sides by 4:

|2x - 3| = 13

We can get two different equations from this:

2x - 3 = 13

and

2x - 3 = -13

So:

2x = 16

2x = -10

x = 8, x = -5

The solution set is {8, -5}