Question

Solve the inequality: |2x+5|>0.5

Answer 1

Explanation:

Divide all three terms by 2 to isolate x:

|x + 5/2| > 0.25

Case 1: x + 5/2 > 0.25 (no absolute value symbol needed), or x > -2.25

Case 2: -(x + 5/2) > 0.25. Multiplying both sides by -1 yields

x + 5/2 < -0.25. Subtracting 5/2 from both sides: x < 5.45

The solution set is -2.25 < x < 5.45.

Answer 2

x < - 2.75, and x > - 2.25

Explanation:

Here we can apply the absolute value rule " If say | u | > a, and a > 0, then u < - a, and u > a. " If a were to be less than 0 ( a < 0 ) then their would be infinitely many solutions as the absolute value will always be greater than or equal to 0.

In this case let us consider both options, u < - a, and u > a,

2x + 5 < - 0.5 or 2x + 5 > 0.5 - solving for each of these inequalities we can combine both intervals and receive the solution

2x + 5 < - 0.5 : 2x < - 5.5, x < - 5.5 / 2, x < - 2.75

2x + 5 > 0.5 : 2x > - 4.5, x > - 4.5 / 2, x > - 2.25

Our solution is hence x < - 2.75, and x > - 2.25. Combining each of the intervals we receive our solution. Note that we can't represent this as one compound inequality as their signs differ.