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:

Question

Mathematics

Evelin Blackwell

21 March, 02:10

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:

+4

Answers (1)

Know the Answer?

Madeleine Peterson · 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.