What is the complete set of real values of x that satisfy the inequality \frac{3}{4} - \fr… — ACT

What is the complete set of real values of $x$ that satisfy the inequality $\frac{3}{4} - \frac{2x}{3} > 2$ ?

x < -\frac{15}{8}

Subtracting

\frac{3}{4}

from both sides of the inequality gives

-\frac{2x}{3} > \frac{5}{4}

. Multiplying both sides by

-\frac{3}{2}

and reversing the inequality sign from greater than (

>

) to less than (

<

) yields

x < -\frac{15}{8}

Subtract

\frac{3}{4}

from both sides of the inequality.

-\frac{2x}{3} > \frac{5}{4}

To isolate the term containing the variable

x

on one side of the inequality.

Multiply both sides of the inequality by

-\frac{3}{2}

and reverse the inequality sign.

x < -\frac{15}{8}

Multiplying or dividing an inequality by a negative number requires reversing the direction of the inequality sign.

Solving linear inequalities by isolating the variable and applying the sign reversal rule when multiplying or dividing by a negative value.

Question