MHB Is This an Example of Absolute Value Inequalities?

[mathdad]

Solve the inequality.

| (4 - 5x)/2 | > 1

Can I use the following theorem?

If a > 0, then | u | > a if and only if u < -a or u > a

 

[HallsofIvy]

Yes, you can: either $$\frac{4- 5x}{2}> 1$$ or [math]\frac{4- 5x}{2}< -1[/math]. Continue, with either equation, by multiplying both sides by the positive number, 2.

 

[mathdad]

I can take it from here.

 

[MarkFL]

Solve the inequality.

| (4 - 5x)/2 | > 1

Can I use the following theorem?

If a > 0, then | u | > a if and only if u < -a or u > a

We are given:

$$\left|\frac{4-5x}{2}\right|>1$$

Multiply through by 2/5:

$$\left|x-\frac{4}{5}\right|>\frac{2}{5}$$

Now the solution is easy to read off...:D

 

[mathdad]

Is the question what is known as absolute value inequalities?