Question

X − (5 − 3x) ≤ 2x − 1 Group of answer choices Number line with a filled circle at -1 and shading to the left Number line with a filled circle at -1 and shading to the right Number line with a filled circle at 2 and shading to the right Number line with a filled circle at 2 and shading to the left

Answer 1

Given:

The inequality is

`x-(5-3x)\leq 2x-1`

To find:

The solution of the given inequality.

Solution:

We have,

`x-(5-3x)\leq 2x-1`

`x-5+3x\leq 2x-1`

`4x-5\leq 2x-1`

Subtract 2x from both sides.

`4x-5-2x\leq 2x-1-2x`

`2x-5\leq -1`

Add 5 on both sides.

`2x-5+5\leq -1+5`

`2x\leq 4`

Divide both sides by 2.

`x\leq 2`

It means, the numbers less than 2 or 2 are included in the solution set.

Number on the left side of 2 are less than 2. So, number line with a filled circle at 2 and shading to the left.

Therefore, the correct option is D.