Question

Solve the inequality and draw the solution |r|-3>2

Answer 1

We want to solve the following inequality

`|r|\text{ -3 >2}`

To solve this inequality, we first add 3 on both sides, so we get

`|r|>2+3=5`

So we have the inequality

`|r|>5`

Recall that the absolute value represents the distance from a number to 0. So this means that the number r is greater than 5 or it is less than -5. So we have the following two inequalities

`r>5`
`r<\text{ -5}`

This could be drawn on the number line as follows. Greater than (>) means that the number 5 is on the left, and the less than (<) means that the number -5 is on the right side. So we get the following