For the inequality -2(3x - 4) + 5 > -3x - 12, which inequality represents all possible val… — SAT

For the inequality $-2(3x - 4) + 5 > -3x - 12$ , which inequality represents all possible values of $x$ ?

x < \frac{25}{3}

The correct inequality is obtained by first distributing

-2

to the terms inside the parentheses to get

-6x + 8 + 5 > -3x - 12

. Combining the constants on the left yields

-6x + 13 > -3x - 12

. Adding

3x

to both sides results in

-3x + 13 > -12

, and subtracting 13 from both sides gives

-3x > -25

. Finally, dividing by

-3

and flipping the inequality sign results in the correct solution.

Distribute

-2

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

-6x + 8 + 5 > -3x - 12

Applying the distributive property simplifies the expression.

Combine the constant terms on the left side.

-6x + 13 > -3x - 12

Simplifying the constant terms makes it easier to isolate the variable.

Add

3x

to both sides to move all variable terms to the left side.

-3x + 13 > -12

This isolates the variable terms on one side of the inequality.

Subtract 13 from both sides to isolate the variable term.

-3x > -25

This isolates the term containing

x

Divide both sides by

-3

and reverse the direction of the inequality sign.

x < \frac{25}{3}

Dividing by a negative number requires reversing the inequality sign.

Solving linear inequalities in one variable using the distributive property and sign reversal rules.

Question