Question

2. Solve and graph the inequality |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.

Here is my work:
4-v < 5
4-v > -5
-5 < 4 – v < 5
-5 < -4 + v < 5
-5 – (-4) < (-4 + v) - 4 < 5 – (-4)
-1 < v < 9

Did I get it right? If not, please explain why and show me how to do it properly.

Answer 1

You could check your own result by choosing one or more numerals from -1 < v < 9, substituting them into the original inequality, and then determining whether the ineq. is then true or false.

Example: v=0: |4 – v| < 5 becomes |4| < 5. Is this true or false?

Answer 2

How do I solve it the right way?

Answer 3

You have the right steps and answer @Liv2952 for part (a) and (b)

Here's another way to do it


Solving the first part leads to
4-v < 5
4-v+v < 5+v
4 < 5+v
4-5 < 5+v-5
-1 < v
v > -1


And solving the second part leads to
4-v > -5
4-v+v > -5+v
4 > -5+v
4+5 > -5+v+5
9 > v
v < 9


So if v > -1 and v < 9, then this is the same as -1 < v < 9

If you want, you can think of it as -1 < v and v < 9 which combines to -1 < v < 9 in a more compact way to write it.

Answer 4

Do you know how to do part (c) ?

Answer 5

Thank you so much! I'm fine with part c.

Answer 6

Ok awesome. Nice job with the solution and thanks for posting your steps/work.