Absolute Value Equations
Try VividMath Premium to unlock full access
Time limit: 0
Quiz summary
0 of 5 questions completed
Questions:
- 1
- 2
- 3
- 4
- 5
Information
–
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading...
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
Loading...
- 1
- 2
- 3
- 4
- 5
- Answered
- Review
-
Question 1 of 5
1. Question
Illustrate `|x|=3` using a number line.Hint
Help VideoCorrect
Great Work!
Incorrect
Absolute value describes the distance of a number on the number line from `0` without considering which direction from zero the number lies.First, find the possible values of `x``|x|=3` means the distance of `x` from `0` is `3` units. Therefore, `x=3` or `x=-3`Next, plot `3` and `-3` on the number line.`x=3`
`x=-3`
-
Question 2 of 5
2. Question
Solve for `x``|x-5|=11`Hint
Help VideoCorrect
Correct!
Incorrect
Absolute value describes the distance of a number on the number line from `0` without considering which direction from zero the number lies.Since we are finding the absolute value of `x`, form a positive and negative equation and solve for `x` on both equationsPositive:`x-5` `=` `11` `x-5` `+5` `=` `11` `+5` Add `5` to both sides `x` `=` `16` Negative:`x-5` `=` `-11` `x-5` `+5` `=` `-11` `+5` Add `5` to both sides `x` `=` `-6` To check if the values of `x` are correct, substitute the values to the equation and check if its absolute value is `11``x=16``|x-5|` `=` `11` `|16-5|` `=` `11` `x=16` `|11|` `=` `11` `11` `=` `11` The absolute value of `11` is `11` `x=-6``|x-5|` `=` `11` `|-6-5|` `=` `11` `x=16` `|-11|` `=` `11` `11` `=` `11` The absolute value of `-11` is `11` Therefore, the absolute values of `x` is `16` or `-6``x=16` or `-6` -
Question 3 of 5
3. Question
Solve for `x``4|2x-2|-14=10`Hint
Help VideoCorrect
Keep Going!
Incorrect
Absolute Value Standard Form
`|ax+b|=c`First, convert the equation to its standard form`4|2x-2|-14` `=` `10` `4|2x-2|-14` `+14` `=` `10` `+14` Add `14` to both sides `4|2x-2|` `=` `24` `4|2x-2|` `div4` `=` `24` `div4` Divide both sides by `4` `|2x-2|` `=` `6` Since we are solving an absolute value equation, form a positive and negative equation and solve for `x` on both equationsPositive:`2x-2` `=` `6` `2x-2` `+2` `=` `6` `+2` Add `2` to both sides `2x` `=` `8` `2x` `div2` `=` `8` `div2` Divide both sides by `2` `x` `=` `4` Negative:`2x-2` `=` `-6` `2x-2` `+2` `=` `-6` `+2` Add `2` to both sides `2x` `=` `-4` `2x` `div2` `=` `-4` `div2` Divide both sides by `2` `x` `=` `-2` `x=4` or `-2` -
Question 4 of 5
4. Question
Solve for `x``-4|1-3/4 x|=-16`Hint
Help VideoCorrect
Fantastic!
Incorrect
Absolute Value Standard Form
`|ax+b|=c`First, convert the equation to its standard form`-4|1-3/4 x|` `=` `-16` `-4|1-3/4 x|` `div(-4)` `=` `-16` `div(-4)` Divide both sides by `-4` `|1-3/4 x|` `=` `4` Since we are solving an absolute value equation, form a positive and negative equation and solve for `x` on both equationsPositive:`1-3/4 x` `=` `4` `1-3/4 x` `-1` `=` `4` `-1` Subtract `1` from both sides `-3/4 x` `=` `3` `-3/4 x` `times(-4)` `=` `3` `times(-4)` Multiply both sides by `-4` `3x` `=` `-12` `3x` `div3` `=` `-12` `div3` Divide both sides by `3` `x` `=` `-4` Negative:`1-3/4 x` `=` `-4` `1-3/4 x` `-1` `=` `-4` `-1` Subtract `1` from both sides `-3/4 x` `=` `-5` `-3/4 x` `times(-4)` `=` `-5` `times(-4)` Multiply both sides by `-4` `3x` `=` `20` `3x` `div3` `=` `20` `div3` Divide both sides by `3` `x` `=` `20/3` `x` `=` `6 2/3` Convert to a mixed number `x=-4` or `6 2/3` -
Question 5 of 5
5. Question
Solve for `y``-7|2y-2|+5=-37`Hint
Help VideoCorrect
Excellent!
Incorrect
Absolute Value Standard Form
`|ax+b|=c`First, convert the equation to its standard form`-7|2y-2|+5` `=` `-37` `-7|2y-2|+5` `-5` `=` `-37` `-5` Subtract `5` from both sides `-7|2y-2|` `=` `-42` `-7|2y-2|` `div(-7)` `=` `-42` `div(-7)` Divide both sides by `-7` `|2y-2|` `=` `6` Since we are solving an absolute value equation, form a positive and negative equation and solve for `x` on both equationsPositive:`2y-2` `=` `6` `2y-2` `+2` `=` `6` `+2` Add `2` to both sides `2y` `=` `8` `2y` `div2` `=` `8` `div2` Divide both sides by `2` `y` `=` `4` Negative:`2y-2` `=` `-6` `2y-2` `+2` `=` `-6` `+2` Add `2` to both sides `2y` `=` `-4` `2y` `div2` `=` `-4` `div2` Divide both sides by `2` `y` `=` `-2` To check if the values of `y` are correct, substitute the values to the equation and check if its absolute value is `-37``y=4``-7|2y-2|+5` `=` `-37` `-7|2(4)-2|+5` `=` `-37` `y=4` `-7|8-2|+5` `=` `-37` `-7|6|+5` `=` `-37` `-7(6)+5` `=` `-37` The absolute value of `6` is `6` `-42+5` `=` `-37` `-37` `=` `-37` `y=-2``-7|2y-2|+5` `=` `-37` `-7|2(-2)-2|+5` `=` `-37` `y=-2` `-7|-4-2|+5` `=` `-37` `-7|-6|+5` `=` `-37` `-7(6)+5` `=` `-37` The absolute value of `-6` is `6` `-42+5` `=` `-37` `-37` `=` `-37` Therefore, the absolute values of `y` is `4` or `-2``y=4` or `-2`