Which of the following represents the solution set for the inequality below?

-3(x - 2) + 5x > 6x - 10

The correct answer is

x < 4

The correct solution is achieved by properly expanding the expression, isolating the variable

x

, and correctly reversing the inequality symbol when dividing both sides by a negative number (

-4

Distribute the

-3

into the parentheses.

-3x + 6 + 5x > 6x - 10

Expanding the terms allows for the combination of like variables.

Combine like terms on the left side of the inequality.

2x + 6 > 6x - 10

Simplifying the expression makes it easier to isolate the variable.

Subtract

6x

from both sides of the inequality.

-4x + 6 > -10

This step groups all variable terms onto one side of the inequality.

Subtract

6

from both sides.

-4x > -16

This isolates the variable term completely.

Divide both sides by

-4

and reverse the inequality sign.

x < 4

Dividing or multiplying an inequality by a negative number requires flipping the inequality direction.

Solving one-variable inequalities requiring distribution and division by a negative coefficient.

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