Question

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

Answer 1

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

Answer 2

Two solutions,
x=7
x=-1
So, D would be your answer.