Question

The difference of –3.2 and the sum of a number and 19.1 is at most 14.2.

A: Negative 3.2 minus (x + 19.1) less-than-or-equal-to 14.2
B: Negative 3.2 minus x + 19.1 less-than-or-equal-to 14.2
C: Negative 3.2 minus (x + 19.1) greater-than-or-equal-to 14.2
D: Negative 3.2 minus x + 19.1 greater-than-or-equal-to 14.2

Answer 1

C

Explanation:

Answer 2

A

Explanation:

The difference of –3.2 and the sum of a number and 19.1 is given as:

|-3.2 - (x + 19.1)| ≤ 14.2

Simplifying the left side of the inequality:

|-22.3 - x| ≤ 14.2

The absolute value of a number is always greater than or equal to 0, so we can split the inequality into two cases:

Case 1: -22.3 - x ≤ 14.2

-36.5 ≤ x

Case 2: -22.3 - x ≥ -14.2

-8.1 ≥ x

Combining the two cases, we get:

-36.5 ≤ x ≤ -8.1

Therefore, the correct option is:

A: Negative 3.2 minus (x + 19.1) less-than-or-equal-to 14.2.