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Home > A2C > Chapter 5 > Lesson 5.2.1 > Problem 5-62


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

  1. Solve for to find the boundary point(s).

    Since , plot on a number line.
    Since makes the inequality true, shade the point.

    Number line, closed point on negative 4.

    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 :

    If you choose :


    Shade the points that are on the true side, to the right of .

    Added to number line, arrow starting at negative 4, point right.

  1. Solve for to find the boundary point(s).

    Plot the boundary points on a number line. Since the points do not make the inequality true, do not shade them.

    Number line, open points on negative 3 halves, &. 4.

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

    If you choose :

    Shade the points between the boundary points, the true region.

    Added to number line, shading between the open points