Question

Solve the equation
3|2x-1|+2=17

Answer 1

the solutions are {-2, 3}

Explanation:

First combine the constants 2 and 17:

3|2x-1|+2=17 => 3|2x - 1| = 15

Next, divide both sides by 3. We get:

3|2x - 1| = 15 => |2x - 1| = 5

We want to solve for x, so divide all three terms by 2 as follows:

|x - 1/2| = 5/2

This equation has two solutions. We regard 1/2 as the "center." The equation tells us that x is either 5/2 greater than this 1/2 or 5/2 smaller:

x = 1/2 + 5/2 = 6/2, or x = 3

and:

x = 1/2 - 5/2 = -4/2 = -2

Thus, the solutions are {-2, 3}