Absolute Value Equations with Sums
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- (Video) Absolute Value Equations by yaymath This video by yaymath goes over absolute value equations. Summary\large{\text{Summary}}Summary Watch the first couple problems to see…
By Alex Federspiel, Zora Gilbert, Victor Wang, Amy Feraco, Jonathan Heller, Anusha Rahman
- Expressions inside of an absolute value become nonnegative. For instance a negative number becomes positive. Let's look at a few examples of how to perform addition in expressio…
By Hannah Bonville, Zora Gilbert, Alex Federspiel, Moor Xu, Victor Wang, Jonathan Heller, Anusha Rahman
Problems 25
- Solve for xxx. ∣5(x−3)−6∣=14|5(x-3)-6|=14∣5(x−3)−6∣=14
- Solve for xxx. ∣(−3)+x−7∣=5|(-3)+x-7|=5∣(−3)+x−7∣=5
- Solve for xxx. ∣16−20∣=x|16-20|=x∣16−20∣=x
- Solve for xxx. ∣x−8∣=13|x-8|=13∣x−8∣=13
- Solve for xxx. ∣−x−20∣+2=2|-x-20|+2=2∣−x−20∣+2=2
- Solve for xxx. ∣x+5∣+18=19|x+5|+18=19∣x+5∣+18=19
- Find the value(s) of xxx such that ∣∣x+3∣−6∣=7.||x+3|-6|=7.∣∣x+3∣−6∣=7.
- What is the average value of the roots of the equation ∣x−10∣=π|x - 10| = \pi∣x−10∣=π?
- What is the positive difference between the largest and smallest roots of the equation ∣x−10∣=15|x - 10| = 15∣x−10∣=15?
- Assume ccc is a positive real number. Which values of xxx satisfy the following equation? ∣x−c∣=∣x∣|x - c| = |x|∣x−c∣=∣x∣
- Solve the absolute value equation ∣x−2∣=∣x−5∣|x-2| = |x-5|∣x−2∣=∣x−5∣ for xxx.
- ∣x∣|x|∣x∣ can be thought of as...
- Does ∣x∣=x|x| = x∣x∣=x?
- Does ∣x∣=−x|x| = -x∣x∣=−x?
- If x=∣12−46∣x = |12-46|x=∣12−46∣, find xxx.
- x=−∣19−3∣x = - |19-3|x=−∣19−3∣ Find xxx.
- 14=∣17−x∣14 = |17-x|14=∣17−x∣ Find all possible values of xxx.
- If 16=∣4−x∣∣4+x∣16 = |4-x||4+x|16=∣4−x∣∣4+x∣, find the smallest possible value of x2x^2x2.
- ∣2x−x2∣=∣3x−x2∣|2x-x^2|=|3x-x^2|∣2x−x2∣=∣3x−x2∣ Find all possible values of xxx.
- Find the value(s) of xxx such that 2−∣x∣=12-|x|=12−∣x∣=1.
- Find the value(s) of xxx such that ∣x+1∣+1=1|x+1|+1 = 1∣x+1∣+1=1.
- Select all the solutions for the following equation: ∣8x+17∣=25|8x+17|=25∣8x+17∣=25
- How many integer solutions are there to the following equation? ∣x∣+∣y∣=−3|x|+|y|=-3∣x∣+∣y∣=−3
- How many integer solutions are there to the following equation? ∣x∣+∣y∣=2|x|+|y|=2∣x∣+∣y∣=2
- How many integer solutions are there to the following equation? ∣x∣+∣y∣=0|x|+|y|=0∣x∣+∣y∣=0