Question

Solve the compound inequality. Graph the solution. –2 ≤ 2x – 4 < 4 (1 point)

Answer 1

1) |3x -7| >= -3

First of all, absolute values are *always* greater than or equal to negative numbers. This implies that the solution set is all real numbers. The "graph" of the solution would be everything on the graph shaded.

2)

(1/3) |2x - 1| < 1

First, multiply both sides by 3.

|2x - 1| < 3

This translates as

-3 < 2x - 1 < 3

Which we solve the compound inequality for x.
Adding +1 to the inequality gives us

-2 < 2x < 4

Dividing by 2 gives us

-1 < x < 2