This is a modulus inequality.
First part: when (6x + 2) is positive
6x + 2 < 10
6x < 10 - 2
6x < 8
x < 8/6
x < 4/3
Second part: when (6x + 2) is negative.
-(6x + 2) < 10 Divide both sides of inequality by -1 and change the sign.
(6x + 2) > -10
6x + 2 > -10
6x > -10 - 2
6x > -12 Divide both sides by 6.
x > -12/6
x > -2.
Combined solution: x < 4/3 and x > -2
-2 < x < 4/3.
Graph is a line on the number line between -2 and 4/3.
-2 and 4/3 are excluded from solution.
The answer is 6.
2x + 4 = 3x - 2
-2x -2x
————————
4 = x - 2
+2 +2
—————
6 = x
We need the length of the sides.
AB=√(2-(-2))²+(4-1)²=√16+9=√25=5; BC=√4²+0=4; CA=√0+9=3. AB+BC+CA=5+4+3=12.
Your answer will turn out to be −4x^2+3x.
