Question

1)lxl+3,2=8 2)lxl-5= 0

Answer 1

1)x=-4,8 x=4,8
2x=5 x=-5

Answer 2

1. To solve the equation |x + 3| = 8, we need to consider two cases:

Case 1: (x + 3) = 8 In this case, we remove the absolute value by considering the positive expression inside the absolute value bars. x + 3 = 8 Subtract 3 from both sides: x = 8 - 3 x = 5

Case 2: -(x + 3) = 8 Here, we consider the negative expression inside the absolute value bars. -x - 3 = 8 Add 3 to both sides: -x = 8 + 3 -x = 11

To isolate x, multiply both sides by -1 to change the sign of -x: x = -11

So, the solution to the equation |x + 3| = 8 is x = 5 and x = -11.

2. The equation |x| - 5 = 0 can be solved as follows:

|x| - 5 = 0 Add 5 to both sides: |x| = 5

To solve for x, we consider two cases:

Case 1: x = 5 In this case, the absolute value of x is positive, so |x| is equal to x. Therefore, x = 5 is a valid solution.

Case 2: -x = 5 Here, the absolute value of x is negative, so |x| is equal to -x. -x = 5 Multiply both sides by -1 to isolate x: x = -5

Therefore, the solutions to the equation |x| - 5 = 0 are x = 5 and x = -5.