Question

9 |x|-2 |x|-8=5 |x| 7 |x|- 2 |x|=3 |x|+12 2 |x|+3 |x|-18= |x|-7 |x| +15

Answer 1

9IxI-2IxI-8=5IxI
IxI×(9-2-5)=8
2|x|=8
|x|=4
x=4;-4

7|x|-2|x|=3|x|+12
|x|×(7-2-3)=12
2|x|=12
|x|=6
x=6;-6

2|x|+3|x|-18=|x|-7|x|+15
|x|×(2+3-1+7)=15+18
11|x|=33
|x|=3
x=3;-3

Answer 2

To solve this equation, let's break it down and consider the absolute value separately for different cases.

Case 1: x ≥ 0 In this case, the absolute value of x is equal to x. Let's rewrite the equation accordingly:

9x - 2x - 8 = 5x + 7x - 2x = 3x + 12 Simplify: 7x - 8 = 12x + 12

Now, isolate the x terms on one side: 7x - 12x = 12 + 8 -5x = 20

Divide by -5 to solve for x: x = -4

Case 2: x < 0 In this case, the absolute value of x is equal to -x. Let's rewrite the equation accordingly:

9(-x) - 2(-x) - 8 = 5(-x) + 7(-x) - 2(-x) = 3(-x) + 12 Simplify: -9x + 2x - 8 = -5x - 7x + 2x = -3x + 12

Now, isolate the x terms on one side: -9x + 2x + 3x = 12 + 8 -4x = 20

Divide by -4 to solve for x: x = -5

Therefore, the solutions to the given equation are x = -4 and x = -5.