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

To solve the inequality –3(2x – 5) < 5(2 – x), we can simplify the left and right sides separately and then solve for x:

–3(2x – 5) < 5(2 – x)

–6x + 15 < 10 – 5x

–6x + 5x < 10 – 15

–x < –5

x > 5

The correct representations of the inequality are:

- x > 5
- –6x + 15 < 10 – x

Option A, -6x - 5 < 10 - x, is not correct because it does not correctly simplify the inequality.

Option B, -6x + 15 < 10 - 5x, is correct as it simplifies to -x < -5 after combining like terms.

Option C is not correct because it is the same as option A.

Option D is not correct because it represents the opposite inequality, x < 5 instead of x > 5.

The correct number line representation is the first option: a number line from negative 3 to infinity, with an open circle at 5 and a bold line pointing to the right.