The solution set for the linear inequality 2(3x - 5) - 4x > 8x - 22 is x > 2. — Armed Services Vocational Aptitude Battery (ASVAB)

The solution set for the linear inequality $2(3x - 5) - 4x > 8x - 22$ is $x > 2$ .

Answer: Answer

The statement is false. The correct solution set is

x < 2

The statement is false because solving the inequality gives

x < 2

. The inequality symbol must be flipped when dividing the final term

-6x > -12

by the negative coefficient

-6

Distribute the

2

across the terms inside the parentheses.

6x - 10 - 4x > 8x - 22

To eliminate the parentheses and prepare the terms for combining.

Combine like terms on the left side of the inequality.

2x - 10 > 8x - 22

To simplify the expression on the left side (

6x - 4x = 2x

Subtract

8x

from both sides.

-6x - 10 > -22

To gather all the variable terms on one side of the inequality.

Add

10

to both sides.

-6x > -12

To isolate the variable term completely.

Divide both sides by

-6

and reverse the inequality sign.

x < 2

Dividing an inequality by a negative number requires flipping the inequality symbol to maintain a mathematically true statement.

Solving multi-step linear inequalities and reversing the inequality symbol when dividing by a negative number.

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