Algebra-1

To determine which absolute value inequality corresponds to the solution set -11 ≤ x ≤ 15, let's analyze each option.

 

Option A, |x - 2| + 6 ≤ 19

|x - 2| + 6 ≤ 19

|x - 2| + 6 - 6 ≤ 19 - 6

|x - 2| ≤ 13

 

Break down the absolute value inequality:

-13 ≤ x - 2 ≤ 13

-13 + 2 ≤ x - 2 + 2 ≤ 13 + 2

-11 ≤ x ≤ 15

This matches the given solution set.

 

Option B, |x - 2| + 6 ≥ 19

|x - 2| + 6 ≥ 19

|x - 2| + 6 - 6 ≥ 19 - 6

|x - 2| ≥ 13

 

Break down the absolute value inequality:

x - 2 ≥ 13 or x - 2 ≤ -13

Solve for x:

For x - 2 ≥ 13:

x - 2 + 2 ≥ 13 + 2

x ≥ 15

For x - 2 ≤ -13:

x - 2 + 2 ≤ -13 + 2

x ≤ -11

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