Absolute Value Expressions
Read this topicExplanations 3
- The absolute value of a number is always positive. It measures the distance of a number or expression from 000. For instance, ∣3∣=3| 3 | = 3∣3∣=3, and ∣–3∣=3| –3 | = 3∣–3∣=3 als…
By Iris, Vatsal Ojha, Amy Feraco, Jonathan Heller, Anusha Rahman
- (Video) Evaluating Expressions Involving Absolute Value by PatrickJMT This video by Patrick JMT covers absolute value expressions. Summary\large{\text{Summary}}Summary Evaluatin…
By Ben Ferrara, Alex Federspiel, Liza Sulkin, Amy Feraco, Jonathan Heller, Anusha Rahman
- Absolute Value Expressions Remember, when you take the absolute value of a number, the result is the non-negative version of that number. For example, ∣12∣=12,|12|=12,∣12∣=12, ∣…
By Caroline K
Problems 27
- Simplify −3−∣5−28∣+6-3-|5-28|+6−3−∣5−28∣+6.
- Simplify –∣–4∣2–| –4 |^2–∣–4∣2.
- Compare the expressions (∣−3∣+∣−5∣−7)(|-3|+|-5|-7)(∣−3∣+∣−5∣−7) and ∣−3−5+7∣|-3-5+7|∣−3−5+7∣.
- If xxx is negative and yyy is positive, is ∣x−y∣×(x−y)|x-y| \times (x-y)∣x−y∣×(x−y) positive or negative?
- True or False\text{True or False}True or False === ∣x−y∣=∣y−x∣|x-y|=|y-x|∣x−y∣=∣y−x∣
- Simplify ∣(−3)3+6∣|(-3)^3+6|∣(−3)3+6∣.
- Simplify ∣−3∣⋅∣−8−6∣4⋅2|-3| \cdot \frac{|-8-6|}{4} \cdot 2∣−3∣⋅4∣−8−6∣⋅2.
- Simplify ∣−3(6)∣2 +∣16∣∣−8∣\frac{|-3(6)|}{2}\ +\frac{|16|}{|-8|}2∣−3(6)∣ +∣−8∣∣16∣.
- Simplify ∣x−∣y−∣−x−y∣∣∣+∣x−∣x+∣y+∣y∣−x−x∣−y∣∣|x-|y-|-x-y|||+|x-|x+|y+|y|-x-x|-y||∣x−∣y−∣−x−y∣∣∣+∣x−∣x+∣y+∣y∣−x−x∣−y∣∣ where x=2x=2x=2 and y=3y=3y=3.
- Using <<<, >>>, or ===, compare ∣5−3∣|5-3|∣5−3∣ and ∣3−5∣|3-5|∣3−5∣.
- Assume x<0x < 0x<0. Simplify the following expression: x−∣x+∣x−∣x∣∣∣.x - \left|x + \left|x - \left|x\right|\right|\right|.x−∣x+∣x−∣x∣∣∣.
- ∣2∣=?|2| = ?∣2∣=?
- ∣−2∣=?|-2| = ?∣−2∣=?
- Simplify ∣x+y∣∣−x−y∣\frac{|x+y|}{|-x-y|}∣−x−y∣∣x+y∣ where x≠−y.x \neq -y.x=−y.
- Simplify ∣x2−1∣∣1−x∣\frac{|x^2-1|}{|1-x|}∣1−x∣∣x2−1∣ if x≠1x \neq 1x=1
- Evaluate ∣x+2∣∣x∣∣y−1∣∣1−y∣\frac{|x+2||x||y-1|}{|1-y|}∣1−y∣∣x+2∣∣x∣∣y−1∣ if x=−1x=-1x=−1 and y≠1.y \neq 1.y=1.
- Simplify ∣4−10(9)+∣−81∣∣|4-10(9)+|-81||∣4−10(9)+∣−81∣∣
- Will the following be positive or negative? Assume x≠0x \neq 0x=0. (−∣−x∣−∣x∣)(∣−x∣+∣−x∣)(-|-x|-|x|)(|-x|+|-x|)(−∣−x∣−∣x∣)(∣−x∣+∣−x∣)
- Simplify ∣(−x)(−y)(z)∣∣(x)(y)(−z)∣\frac{|(-x)(-y)(z)|}{|(x)(y)(-z)|}∣(x)(y)(−z)∣∣(−x)(−y)(z)∣ if x,y,zx, y, zx,y,z are nonzero.
- Simplify ∣(4)(−6)∣∣4−6∣|(4)(-6)||4-6|∣(4)(−6)∣∣4−6∣
- True or False\text{True or False}True or False === ∣−x−y∣=∣x+y∣|-x-y|=|x+y|∣−x−y∣=∣x+y∣
- Simplify the expression. 6−∣−3⋅4∣−∣8∣6-|-3\cdot 4|-|8|6−∣−3⋅4∣−∣8∣
- Simplify the expression. ∣14÷(−∣−3−4∣)+1∣−3|14\div(-|-3-4|)+1|-3∣14÷(−∣−3−4∣)+1∣−3
- Simplify the expression. 3÷∣1−4∣+∣9÷∣−3−6∣∣3\div|1-4|+|9\div|-3-6||3÷∣1−4∣+∣9÷∣−3−6∣∣
- Simplify the expression. ∣∣∣−3+7∣−8∣+9∣|||-3+7|-8|+9|∣∣∣−3+7∣−8∣+9∣
- Simplify the expression. ∣−6÷3⋅4−2∣|-6\div3\cdot 4-2|∣−6÷3⋅4−2∣
- The absolute value of any real number is...