Question

Suppose x = -2 and y = 8. Select all the inequalities that are true. A. |x| ≤ Iy| B. |y| ≤ |x| C. lx| > lyl D. |y| < |x| E. x < y

Answer 1

Explanation:

To determine which inequalities are true, let's evaluate each option using the given values of x = -2 and y = 8.

A. |x| ≤ |y|:

|x| = |-2| = 2, and |y| = |8| = 8. Since 2 is less than or equal to 8, this inequality is true.

B. |y| ≤ |x|:

|y| = |8| = 8, and |x| = |-2| = 2. Since 8 is greater than or equal to 2, this inequality is false.

C. |x| > |y|:

|x| = |-2| = 2, and |y| = |8| = 8. Since 2 is not greater than 8, this inequality is false.

D. |y| < |x|:

|y| = |8| = 8, and |x| = |-2| = 2. Since 8 is not less than 2, this inequality is false.

E. x < y:

Since x = -2 and y = 8, -2 is indeed less than 8. Therefore, this inequality is true.

Based on the given values of x and y, the inequalities that are true are:

A. |x| ≤ |y|

E. x < y

I hope this helps!