Absolute Value Equations with Products
Read this topicExplanations 3
- Variables Simple cases Absolute value equations with products are similar to absolute value equations with sums. The process is identical in the most basic examples. For example…
By Zora Gilbert, Amy Feraco, Jonathan Heller, Caroline K, Anusha Rahman
- Absolute values make the expression within nonnegative. Earlier, we saw absolute values with sums. Let's look at a few examples of how to perform multiplication with absolute va…
By Hannah Bonville, Zora Gilbert, Alex Federspiel, Victor Wang, Liza Sulkin, Amy Feraco, Jonathan Heller, Caroline K, Anusha Rahman
- (Video) Solving a multi step absolute value equation by Brian McLogan This video by Brian McLogan works through a complex absolute value problem. Summary\large{\text{Summary}}Su…
By Amy Feraco, Victor Wang, Jonathan Heller, Caroline K
Problems 22
- Solve for xxx. 12∣x∣=412|x|=412∣x∣=4
- Solve for xxx. ∣x2∣=20\left|\frac{x}{2}\right|=202x=20 Select all options that apply.
- If α∣x4∣=5\alpha\left|\frac{x}{4}\right|=5α4x=5 where α\alphaα is a positive constant, find all possible values of xxx.
- Solve for xxx. −3∣5x∣=−17-3|5x|=-17−3∣5x∣=−17
- Solve for xxx. 12∣2x∣=6\frac{12}{|2x|}=6∣2x∣12=6
- Solve for xxx. 9∣110(−x)∣=2.79\left|\frac{1}{10} (-x)\right|=2.79101(−x)=2.7
- Solve for xxx. ∣−18×12x∣=900\left|-18\times\frac{1}{2} x\right|=900−18×21x=900
- How many distinct hyperbolas does the graph of the equation ∣x∣2⋅∣y∣2=1|x|^2\cdot |y|^2 = 1∣x∣2⋅∣y∣2=1 contain?
- When does 3∣x∣=3x3|x| = 3x3∣x∣=3x? Select all options that apply.
- When does 3∣−x∣=3(−x)3\lvert -x\rvert = 3(-x)3∣−x∣=3(−x)? Select all options that apply.
- When does 3∣−x∣=3x3\lvert -x\rvert = 3x3∣−x∣=3x? Select all options that apply.
- When does ∣x∣⋅∣−x∣=x⋅x\lvert x\rvert\cdot\lvert -x\rvert = x \cdot x∣x∣⋅∣−x∣=x⋅x? Select all answers that apply.
- When does ∣x∣⋅∣−x∣=−x⋅x\lvert x\rvert\cdot \lvert-x\rvert = -x\cdot x∣x∣⋅∣−x∣=−x⋅x? Select all that apply.
- Solve for xxx in the equation 6∣x∣=186|x|=186∣x∣=18. Select all options that apply.
- Solve for xxx in the equation 8∣x∣=48|x|=48∣x∣=4. Select all options that apply.
- Solve for xxx in the equation 24∣x∣=624|x|=624∣x∣=6.
- Solve for xxx in the equation 6∣x∣=−66|x|= -66∣x∣=−6. Select all options that apply.
- Solve for xxx in the equation 5∣x∣−4=∣x∣−25|x| - 4 = |x| - 25∣x∣−4=∣x∣−2. Select all options that apply.
- Is ∣3∣×∣−14∣|3|\times |-14|∣3∣×∣−14∣ equivalent to ∣3×(−14)∣|3\times (-14)|∣3×(−14)∣?
- Find all real numbers xxx such that the equation ∣−x∣=−x\lvert -x\rvert = -x∣−x∣=−x holds. Choose the best answer.
- Find the value(s) of xxx such that 2÷∣x∣=12\div|x| = 12÷∣x∣=1.
- Find the value(s) of xxx such that 2÷∣2x∣=22\div|2x| = 22÷∣2x∣=2.