What value of x is in the solution set of 3(x – 4) ≥ 5x + 2?

Hey!

To start solving equation, we should first distribute the parenthesis. We do this so that we can get rid of the parenthesis.

Original Equation :
3 ( x - 4 ) ≥ 5x + 2

New Equation {Changed by Distribution} :
3x - 12 ≥ 5x + 2

Next, we'd add 12 to both sides of the equation to get rid of the 12 on the left side of the equation.

Old Equation :
3x - 12 ≥ 5x + 2

New Equation {Changed by Adding 12 to Both Sides} :
3x ≥ 5x + 14

Now we subtract 5x from both sides of the equation to get rid of the 5x from the right side.

Old Equation :
3x ≥ 5x + 14

New Equation {Changed by Subtracting 5x From Both Sides} :
-2x ≥ 14

Now we must inverse the inequality. To do that we multiply both sides by -1.

Old Equation :
-2x ≥ 14

New Equation {Changed by Inverse} :
2x ≤ -14

Just by looking at the equation, you can easily tell that it needs to be simplified. So, that's what we'll do next.

Old Equation :
2x ≤ -14

New Equation {Changed by Dividing Both Sides by Two} :
x ≤ -7

Seeing as the equation cannot be simplified any further, we have our answer.
The value of x in the inequality of 3 ( x – 4 ) ≥ 5x + 2, is  x ≤ -7.

Hope this helps!

- Lindsey Frazier ♥