Approaches to Solving Absolute Value Inequalities
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- (Videos) Solving Absolute Value Inequalities by PatrickJMT Method 1: GREATER THAN When solving absolute value inequalities, what steps you take are different depending on whethe…
By Ben Ferrara, Zora Gilbert, Alex Federspiel, Amy Feraco, Dani, Anusha Rahman
- The Rules There are two rules to follow when you've got an inequality with an absolute value. If your simplified inequality looks like ∣x∣>y|x| > y∣x∣>y, then set up and solve t…
By Hannah Bonville, Zora Gilbert, Alex Federspiel, Dani, Anusha Rahman
- Solving Absolute Value Inequalities There are two simple rules when tackling absolute value inequalities. Techniques for solving inequalities extend to those involving powers an…
By Anusha Rahman
Problems 45
- Solve for xxx: ∣x−1∣<3|x-1| < 3∣x−1∣<3
- Solve for xxx: ∣2x∣>4|2x| > 4∣2x∣>4
- Find the value(s) of xxx such that ∣−4x+18∣<6\lvert-4x+18\rvert < 6∣−4x+18∣<6.
- Solve for xxx. ∣x2−6x+9∣>0|x^2-6x+9| > 0∣x2−6x+9∣>0
- Solve for xxx. ∣4x−6∣<6|4x-6|<6∣4x−6∣<6
- Solve for xxx. ∣4x−8∣≥6|4x-8|\geq6∣4x−8∣≥6
- Solve for xxx. ∣9x+2∣+6<10|9x+2|+6<10∣9x+2∣+6<10
- Solve for xxx. ∣x−24∣+3≤8\left|\frac{x-2}{4}\right|+3\leq84x−2+3≤8
- Solve for xxx. 17 ∣5x−3∣−2>3\frac{1}{7} \ |5x-3|-2>371 ∣5x−3∣−2>3
- Solve for xxx. 2∣4x−1∣+6≥202|4x-1|+6\geq202∣4x−1∣+6≥20
- Solve for xxx. 2∣x6+7∣+1<102\left\lvert\frac{x}{6} +7\right\rvert+1<1026x+7+1<10
- Solve for xxx. ∣4x−20∣<5|4x-20|<5∣4x−20∣<5
- Solve for xxx. ∣10x+17∣≤−4|10x+17|\leq-4∣10x+17∣≤−4
- Solve for xxx. ∣7−9x∣≥10|7-9x|\geq10∣7−9x∣≥10
- Solve for xxx. 175∣1311x−97∣−62>95\frac{17}{5}\left|\frac{13}{11}x-\frac{9}{7}\right|-\frac{6}{2}>\frac{9}{5}5171113x−79−26>59 Round to the nearest tenth.
- Solve for xxx. 8∣2x−17∣+9<178|2x-17|+9<178∣2x−17∣+9<17
- Solve for xxx. 13 ∣9x+6∣−14<8\frac{1}{3} \ |9x+6|-14<831 ∣9x+6∣−14<8
- Solve for xxx. 8∣14x+3∣−16≤1208|14x+3|-16\leq1208∣14x+3∣−16≤120
- How many ordered pairs of integers (x,y)(x, y)(x,y) are there such that 0<∣xy∣<36?0 < \left\vert xy \right\vert < 36?0<∣xy∣<36? Source: Math Prize for Girls
- Assume ∣3x−2∣≤6|3x - 2| \le 6∣3x−2∣≤6. If x∈Zx \in \mathbb{Z}x∈Z (i.e. xxx is an integer), then how many possible values of xxx are there?
- Assume ∣4x−2∣≤3|4x-2| \le 3∣4x−2∣≤3. If x∈Zx \in \mathbb{Z}x∈Z (i.e. xxx is an integer), then how many possible values of xxx are there?
- Assume ∣x−2∣≤∣x2−3∣|x-2| \le |\frac{x}{2} - 3|∣x−2∣≤∣2x−3∣. If x∈Zx \in \mathbb{Z}x∈Z (i.e. xxx is an integer), then how many possible values of xxx are there?
- Which of these intervals is the set of all solutions to ∣x3∣≤∣x2∣|x^3| \le |x^2|∣x3∣≤∣x2∣?
- What integer value of xxx satisfies the following equation? ∣3x−25∣<5|3^x - 25| < 5∣3x−25∣<5
- ∣log2(x4−3)+1∣≤1| \log_2(\frac{x}{4}-3) + 1 | \le 1∣log2(4x−3)+1∣≤1 The values of xxx which satisfy this equation are an interval [a,b][a, b][a,b]. What is b−ab-ab−a?
- Solve for xxx. ∣ln(x)∣<3\lvert\ln(x)\rvert<3∣ln(x)∣<3
- Solve ∣x+5∣<6|x+5|<6∣x+5∣<6.
- Solve ∣x−3∣<7|x-3|<7∣x−3∣<7.
- Solve ∣x−2∣≥3|x-2|\geq3∣x−2∣≥3.
- Solve ∣x+4∣≥2|x+4|\geq2∣x+4∣≥2.
- Solve ∣3x+9∣<4|3x+9|<4∣3x+9∣<4.
- Solve ∣2x−9∣≤8|2x-9|\leq8∣2x−9∣≤8.
- Solve for xxx. ∣x∣<1|x|<1∣x∣<1
- Solve for xxx. ∣x∣>1|x|>1∣x∣>1
- Solve for xxx. ∣x∣≤1|x|\leq1∣x∣≤1
- Solve for xxx. ∣x∣≥1|x|\geq1∣x∣≥1
- Solve for xxx. ∣x∣<0|x|<0∣x∣<0
- Solve for xxx. ∣x−3∣<4|x-3|<4∣x−3∣<4
- Solve for xxx. ∣x+3∣>4|x+3|>4∣x+3∣>4
- Solve for xxx. ∣x+6∣≤2|x+6|\leq2∣x+6∣≤2
- Solve for xxx. ∣x+2∣≥1|x+2|\geq1∣x+2∣≥1
- Solve for xxx. ∣x+9∣<−12|x+9|<-12∣x+9∣<−12
- Solve for xxx. ∣2x+1∣≥3|2x+1|\geq3∣2x+1∣≥3
- Solve for xxx. ∣3x+2∣<4|3x+2|<4∣3x+2∣<4
- Describe the solutions of the following inequality: ∣8x+2∣≤1|8x+2|\leq{1}∣8x+2∣≤1