jameslee2798
Answered

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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

Sagot :

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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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

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Answer:

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

Step-by-step explanation:

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