Question

mrs. miller gave the following inequality for her students to solve.

$-3(7x + 11) < 2(2x - 4)$

what is the solution set to the inequality?

a $x < 1$

b $x < -1$

c $x > -1$

d $x < -3$

Explanation:

Step1: Expand both sides

$-3(7x+11) = -21x - 33$; $2(2x-4) = 4x - 8$
Inequality becomes: $-21x - 33 < 4x - 8$

Step2: Move x terms to left

Subtract $4x$ from both sides:
$-21x - 4x - 33 < -8$
$-25x - 33 < -8$

Step3: Move constants to right

Add 33 to both sides:
$-25x < -8 + 33$
$-25x < 25$

Step4: Divide by -25, flip sign

$\frac{-25x}{-25} > \frac{25}{-25}$
$x > -1$

Answer:

C. $x > -1$