For which values of x is the inequality -4(2x - 5) \geq 3x + 9 true? — SAT

For which values of $x$ is the inequality $-4(2x - 5) \geq 3x + 9$ true?

The inequality is true for all values of

x

such that

x

is less than or equal to

1

The correct inequality representing the solution set is the one that shows the variable is less than or equal to one.

Distribute the factor of

-4

to the terms inside the parentheses on the left side of the inequality.

-8x + 20 \geq 3x + 9

Applying the distributive property gives

-4 \times 2x = -8x

and

-4 \times -5 = 20

Subtract

3x

from both sides of the inequality to collect all terms with the variable

x

on the left side.

-11x + 20 \geq 9

Grouping the variable terms helps isolate the variable.

Subtract

20

from both sides of the inequality to isolate the variable term.

-11x \geq -11

Subtracting twenty from both sides moves the constant terms to the right side of the inequality.

Divide both sides by

-11

and reverse the direction of the inequality sign.

x \leq 1

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

Linear Inequalities in One Variable

Question