Question

Pretty Easy questions. Answer for lots of points.

Simplify (Write each expression without using the absolute value symbol)
1) |x+3| if x > 5
2) |x+3| if x > 2
3) |x-3| if x > 5
4) |120+x| if x < -120
5) |x-120| if x <-120
6) |x-(-12)| if x > -12
7) |x-(-12)| if x < -12
8) |x-(-12)| if x = -12
9) |x / 3| if x > 0
10) |x / 3| if x < 0

Answer 1

Answers in bold

1. x+3
2. x+3
3. x-3
4. -x-120
5. -x+120
6. x+12
7. -x-12
8. 0
9. x/3
10. -x/3

Ignore the non bold numbers up front as they are just meant to keep track of which answer goes where. The result to problem 8 is zero, while everything else involves x somehow.

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Step-by-step explanation:

Use a graphing tool like Desmos to see that y = |x+3| is a V shaped graph. The vertex is at (-3,0). Stuff to the right of the vertex is x > -3. The interval x > 5 is a subset of the previous inequality.

In other words, if you pick something larger than 5, then its automatically larger than -3.

The y = |x+3| is composed of the linear equations y = x+3 and y = -(x+3) depending if you are on the right branch or the left branch respectively.

We go for y = x+3 since we're on the right hand side.

Use this type of trick to answer the others in this fashion.

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For problem 8, we replace x with -12 and compute like so

|x-(-12)| = |x+12| = |-12+12| = |0| = 0