Question

Solve -2x + 1 ≤ -7 and describe the graph of the solution.

x ≤ 4; closed circle on 4, shading to the left

x ≥ 4; closed circle on 4, shading to the right

x ≥ 4; open circle on 4, shading to the right

x ≤ 4; open circle on 4, shading to the left

Answer 1

Okay, here's how I work these:

1) find the dividing point(s). Change the inequality to an equality and solve.
\[-2x+1 = -7\]\[-2x=-8\]\[x=?\]

2) find the appropriate dividing point marker. If the inequality has an equals sign in it (\(\le,\ge\)) we are including the point, so we use a filled circle, otherwise, we use an open circle (does not include the point).

3) Try test points as needed to find the appropriate part to shade. I like to use 0 whenever possible, because the arithmetic is usually easier. If 0 makes the inequality true, then shade the portion that contains 0, otherwise shade the other part.

With these steps, you should be able to do the problem above in less time than it took me to type this, and I'm a fast typist!