Answer:
x < 3 ∪ x > 13
Step-by-step explanation:
|-8+x|>5 is an absolute value inequality and has two valid solutions.
One way of solving this is to write two separate inequalities equivalent to |-8+x|>5:
Case 1: -8+x is already positive. Then the absolute value operator is unneeded, and -8+x >5. Adding 8 to both sides, we get x > 13.
Case 2: -8+x is negative. Then |-8+x| = -1(-8+x), or 8 - x. Then 8 - x > 5. It's best to solve such an inequality so that x comes out positive, so we add x to both sides: 8 > 5 + x. Finally, we solve for x by subtracting 5 from both sides:
3 > x.
Thus, the solution to |-8+x|>5 has two parts: x < 3 and x > 13.
Check: suppose we choose a number from the set x < 3 and determine whether the original inequality is true or false. Choose x = 0. Is 0 < 3 true? Yes, it is. Next, choose a number from the set x > 13: x = 20. Is 20 > 13 true? Yes, it is.
Thus, our solution is correct: x < 3 ∪ x > 13
