Question

7
which inequality describes all the solutions?
5(3 - x) < -2x + 6
options:
x > 7
x > 3
x < 3
x < 9
clear all

Explanation:

Step1: Expand the left side

Expand \( 5(3 - x) \) to get \( 15 - 5x \). So the inequality becomes \( 15 - 5x < -2x + 6 \).

Step2: Move terms with \( x \) to one side

Add \( 5x \) to both sides: \( 15 < 3x + 6 \).

Step3: Isolate the term with \( x \)

Subtract 6 from both sides: \( 9 < 3x \).

Step4: Solve for \( x \)

Divide both sides by 3: \( 3 < x \), which is \( x > 3 \).

Answer:

\( x > 3 \) (corresponding to the option with \( x > 3 \))