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 ♥
