Question

What is the solution to −6x−4≥−2(x−4) ?

x≤−3

x≥3

x≥2

x≤−1

Answer 1

The correct answer is: Option 1: x≤-3

Explanation:

Given inequality is:

`-6x-4\geq -2(x-4)`

First of all, we will distribute -2 into the bracket

`-6x-4\geq -2x+8`

Then we will add 4 on both sides

`-6x-4+4\geq -2x+8+4\\-6x \geq -2x+12`

Adding 2x on both sides

`-6x+2x\geq -2x+12+2x\\-4x\geq 12`

Dividing both sides by 4

`(-4x)/(4) \geq (12)/(4)\\-x \geq 3`

As there should be only x on the left side of the inequality we will multiply the inequality with -1.

Multiplying the inequality with -1 reverses the sign of inequality

So,

`x \leq -3`

Hence,

The correct answer is: Option 1: x≤-3