Answers in bold
- x+3
- x+3
- x-3
- -x-120
- -x+120
- x+12
- -x-12
- 0
- x/3
- -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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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
