Answer:
The correct answer is: Option 1: x≤-3
Step-by-step explanation:
Given inequality is:
[tex]-6x-4\geq -2(x-4)[/tex]
First of all, we will distribute -2 into the bracket
[tex]-6x-4\geq -2x+8[/tex]
Then we will add 4 on both sides
[tex]-6x-4+4\geq -2x+8+4\\-6x \geq -2x+12[/tex]
Adding 2x on both sides
[tex]-6x+2x\geq -2x+12+2x\\-4x\geq 12[/tex]
Dividing both sides by 4
[tex]\frac{-4x}{4} \geq \frac{12}{4}\\-x \geq 3[/tex]
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,
[tex]x \leq -3[/tex]
Hence,
The correct answer is: Option 1: x≤-3
