Question

Solve −4x−4≤0 or 4x−4≤5 and write the solution in interval notation.

Answer 1

{-1, 9/4].

Explanation:

-4x - 4 ≤ 0

4x - 4 ≤ 5

From the first equation:

-4x ≤ 4

x ≥ -1.

From the second:

4x ≤ 9

x ≤ 9/4.

Answer 2

Explanation:

Solve each inequality to find

-4x - 4 ≤ 0

-4x ≤ 4

x ≥ -1.

and

4x − 4 ≤ 5

4x ≤ 9

x≤ 9/4

Graph each solution. Then, graph the numbers that make either of the inequalities true. The final graph will show all the numbers that make either inequality true, which are the numbers shaded on either of the first two graphs.

In interval notation, we write this as (−∞,∞).