Inequalities: Compound And Absolute Value

1) * Solve:

3 x space minus space 2 space less than space 1 space space space o r space space space 5 x space plus space 1 space greater or equal than space 11

X < 1 or x ≥ 2

1 < x < 2

X < 2 or x ≥ 1

No solution!

The given answer, "x

Explanation

The given answer, "x

2) * Solve:

minus 5 space less or equal than space 2 w space minus space 3 space less than space 7

-1 ≤ w < 5

-2 ≤ w < 10

W ≤ -1 or w ≥ 5

No solution!

The given inequalities state that w must be greater than or equal to -1 and less than 5. This means that w can take any value between -1 and 5, including -1 but not including 5. Therefore, the correct answer is -1 ≤ w

Explanation

The given inequalities state that w must be greater than or equal to -1 and less than 5. This means that w can take any value between -1 and 5, including -1 but not including 5. Therefore, the correct answer is -1 ≤ w

3) * Solve:

open vertical bar x minus 3 close vertical bar greater than 2

X < 1 or x > 5

1 < x < 5

X < -1 or x > -5

X < -5 or x > -1

The given answer x 5 is correct because it represents the correct solution to the given inequality x 5. This means that x can be any value that is less than 1 or greater than 5.

Explanation

The given answer x 5 is correct because it represents the correct solution to the given inequality x 5. This means that x can be any value that is less than 1 or greater than 5.

4) * Solve: $open vertical bar 2 k space minus 1 close vertical bar space greater or equal than 5$

K ≤ - 2 or k ≥ 3

-2 ≤ k ≤ 3

K ≤ -3 or k ≥ 2

-3 ≤ k ≤ 2

The correct answer is k ≤ -2 or k ≥ 3. This is because the given inequality represents two separate ranges for the variable k. The first range, k ≤ -2, includes all values of k that are less than or equal to -2. The second range, k ≥ 3, includes all values of k that are greater than or equal to 3. Therefore, the correct answer is the combination of these two ranges, k ≤ -2 or k ≥ 3.

Explanation

The correct answer is k ≤ -2 or k ≥ 3. This is because the given inequality represents two separate ranges for the variable k. The first range, k ≤ -2, includes all values of k that are less than or equal to -2. The second range, k ≥ 3, includes all values of k that are greater than or equal to 3. Therefore, the correct answer is the combination of these two ranges, k ≤ -2 or k ≥ 3.

5) Which inequality is represented by the graph below:

not-available-via-ai

Explanation

not-available-via-ai

6) * Solve:

open vertical bar n plus 5 close vertical bar less or equal than 4

-9 ≤ n ≤ -1

N ≤ -9 or n ≥ -1

N ≤ -1 or n ≥ 9

-1 ≤ n ≤ 9

The correct answer is -9 ≤ n ≤ -1. This is because the inequality -9 ≤ n ≤ -1 means that n can take any value between -9 and -1, including -9 and -1 themselves. It satisfies all the given conditions in the question.

Explanation

The correct answer is -9 ≤ n ≤ -1. This is because the inequality -9 ≤ n ≤ -1 means that n can take any value between -9 and -1, including -9 and -1 themselves. It satisfies all the given conditions in the question.