Solve |4-v| < 5
a. Write the inequality as two inequalities without absolute value

B. Solve the inequality and write the solution set.

Relation questions:

a.
4 - v < 5
4 - v > -5 ------ You have to flip the sign and change the 5 to a negative to write the second inequality

b.
4 - v < 5 ----- Subtract 4 from both sides
-v < 1 ------- Divide by -1 and switch the sign since you're dividing by a negative

4 - v > -5 ------ Subtract 4 from both sides
-v > -9 ------ Divide by -1; again, switch the sign

Solution set: -1<v<9 or 9>v>-1

Below the answer for this question, I've written how to solve the other type of inequality.

When the problem is IequationI< n you write it out as: -5<4-v<5

and then solve like a normal equation. The only difference being that if you do something to one side, you have to do it to every other side.

-5<4-v<5 subtracting 4 gives you -9<-v<1 multiply both sides by -1 to make v positive, so you have

!!(always remember to flip the inequalities if you multiply or divide by a negative number)!!

9>v>-1 or -1<v<9

If it's the other type IequationI>n

you write it as two parts.

If you have IxI>5, it's written as x>5 or x<-5. Math teachers expect you to solve both, but that's a pretty easy