Question

In each of the equations or inequalities below, find all the integer values of x that make the equation or the pair of inequalities true. Explain reasoning for each part.
Part A: |x|=17
Value Of X:

Part B: |x+9|=15
Value Of X:

Part C: |x-10| ≤ 13 and |x-10| ≥ 9
(Find the values of x that make both inequalities true)
Values of X:

Answer 1

So in these problems, we're dealing with absolute value. Absolute value is the real amount of the number, or it's real place value without a negative sign. 
Part A: if the absolute value of X was 17, then X could equal -17 or 17.
Part B: |x+9|=15. We know that 6+9=15, so X could equal -6 or 6. 
Part C: |x-10| ≤ 13. We know that 23-10 is 13. So 23 would be the greatest value of X. Then, for the smallest value of X, if we insert -3 in the equation to take the place of the variable, we get |-3-10|=13. So -3 would be the smallest value of the equation. X≤ 23 and X≥-3.