Question

Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?

A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.

Answer 1

based on what he said the answer is b

Explanation:

Answer 2

A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.

Explanation:

Given

`3(8 - 4x) < 6(x - 5)`

Required

Describe the number line

We have:

`3(8 - 4x) < 6(x - 5)`

Open brackets

`24 - 12x < 6x - 30`

Collect like terms

`-12x - 6x < -30 - 24`

`-18x < -54`

Divide by -18 (the inequality changes)

`x > 3`

`>` means that the arrow on the number line points to the right, and it makes use of an open circle that starts from 3.