Solve for x: 3|x - 3| + 2 = 14

A) no solutions

B) X = - 1, x = 8.3

C) x = 0, x = 7

D) x = - 1, x = 7

Two solutions,

x=7

x=-1

So, D would be your answer.

1 Subtract 22 from both sides

3|x-3|=14-23∣x-3∣=14-2

2 Simplify 14-214-2 to 1212

3|x-3|=123∣x-3∣=12

3 Divide both sides by 33

|x-3|=/frac{12}{3}∣x-3∣=

3



12



4 Simplify / frac{12}{3}

3



12

to 44

|x-3|=4∣x-3∣=4

5 Break down the problem into these 2 equations

x-3=4x-3=4

- (x-3) = 4 - (x-3) = 4

6 Solve the 1st equation: x-3=4x-3=4How?

x=7x=7

7 Solve the 2nd equation: - (x-3) = 4 - (x-3) = 4How?

x=-1x=-1

8 Collect all solutions

x=-1,7x=-1,7