### Home > CCA2 > Chapter 4 > Lesson 4.2.1 > Problem 4-65

Find boundary points for each of the following inequalities. Draw the boundaries on a number line and shade the solution regions. Homework Help ✎

Solve for

*x*to find the boundary point(s).3

*x*+ 2 =*x*− 6

2*x*= −8

*x*= −4Since

*x*= −4, plot −4 on a number line.

Since −4 makes the inequality true, shade the point.Test a point on either side of the boundary point in the original inequality and decide if you get a true or false statement.

If you choose

*x*= 0:

3(0) + 2 ≥ (0) − 6

2 ≥ −6 → TrueIf you choose x = −6:

3(−6) + 2 ≥ (−6) − 6

−16 ≥ −12 → FalseShade the points that are on the true side, to the right of −4.

Solve for

*x*to find the boundary point(s).2

*x*^{2}− 5*x*= 12

2x^{2}− 5*x*− 12 = 0Plot the boundary points on a number line. Since the points do not make the inequality true, do not shade them.

Test a point between the boundary points in the original inequality. Decide if the simplified statement is true or false.

If you choose x = 0:

2(0)^{2}− 5(0) < 12

0 < 12 → TrueShade the points between the boundary points, the true region.