Question

Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.

x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.

Answer 1

Correct answers:
- –6x + 15 < 10 – 5x
- The number line with an open circle at 5 and a ray pointing right (represents x > 5)

Reason: -3(2x–5) = -6x+15 and 5(2–x) = 10–5x, so -6x+15 < 10–5x ⇒ x > 5.