Question

2. Solve and graph.

|4 – v| < 5

a. Write the inequality as two inequalities without absolute value.
b. Solve the inequality and write the solution set.
c. Graph the solution on a number line.

Answer 1

OK so when you have absolute values it is very useful to think of abs(4 - v) as the distance between 4 and v.

Then you can write abs(4-v) < 5 as -5 < 4 - v < 5
This is because the distance between these two points must be in this range. Try writing out a real number line and giving random values to v. You will be able to see how this rule works!

Now that we have -5 < 4 - v < 5 we can solve it using basic algebra. We can solve it just like a normal equation but instead of doing an operation on "both sides" we have to do an operation on all three sides :D

-5 < 4 - v < 5
-5 -4 < 4 - v - 4 < 5 -4 add - 4 to all three sides
-9 <-v <1 simplify
-1 * -9 > -1 * -v > -1 * 1 multiply by -1 DONT FORGET TO SWITCH INEQUALITIES
9 > v > -1
-1 < v < 9

now just make sure you show in your number line what numbers v can be.


make sure you know the difference between ( and [