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

The correct representations of the inequality –3(2x – 5) < 5(2 – x) are:

x < 5

and

-6x + 15 < 10 - 5x

Option A (x < 5) is correct because it represents the inequality in terms of the solution set for x.

Option B (-6x + 15 < 10 - 5x) is also correct because it is a valid algebraic manipulation of the original inequality:

-3(2x - 5) < 5(2 - x)

-6x + 15 < 10 - 5x

Simplifying this inequality yields -x < -5, which can be rewritten as x > 5.

The number line from negative 3 to 3 in increments of 1 and the open circle at 5 with a bold line pointing to the right is incorrect because it represents the solution set for x as x > 5, which is the opposite of the correct solution set x < 5.

The number line from negative 3 to 3 in increments of 1 and the open circle at negative 5 with a bold line pointing to the left is also incorrect because it does not represent the solution set for x at all.

Answer 2

The correct representations of the inequality –3(2x – 5) < 5(2 – x) are:

-6x + 15 < 10 – 5x

and

x < 5

The option "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" is not a correct representation of the inequality because it only shows one of the solutions (x < 5) and does not show the other solution (-6x + 15 < 10 – 5x).

The option "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" is not a correct representation of the inequality because it represents the inequality x < -5, which is not a solution to the original inequality.

I Hope This Helps!