## 17Calculus Precalculus - Solving Absolute Value Inequalities

##### 17Calculus

Solving Absolute Value Inequalities

Solving inequalities requires special techniques that you didn't need when you were solving equations.

This guy does a great job of explaining how to solve inequalities containing absolute values.

### MIP4U - Absolute Value Inequalities [10min-29secs]

video by MIP4U

Now try the practice problems.

Practice Solving Inequalities

Unless otherwise instructed, find all values of $$x$$ that solve each inequality.

$$|x-2| < 4$$

Problem Statement

Find the values of $$x$$ that solve the inequality $$|x-2| < 4$$.

$$-2 < x < 6$$

Problem Statement

Find the values of $$x$$ that solve the inequality $$|x-2| < 4$$.

Solution

### Dr Chris Tisdell - 2089 video solution

video by Dr Chris Tisdell

$$-2 < x < 6$$

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$$|3x-2| < 4$$

Problem Statement

Find the values of $$x$$ that solve the inequality $$|3x-2| < 4$$.

$$-2/3 < x < 2$$

Problem Statement

Find the values of $$x$$ that solve the inequality $$|3x-2| < 4$$.

Solution

### Dr Chris Tisdell - 2090 video solution

video by Dr Chris Tisdell

$$-2/3 < x < 2$$

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$$|1-3x| \leq 2$$

Problem Statement

Find the values of $$x$$ that solve the inequality $$|1-3x| \leq 2$$.

$$-1/3 \leq x \leq 1$$

Problem Statement

Find the values of $$x$$ that solve the inequality $$|1-3x| \leq 2$$.

Solution

### Dr Chris Tisdell - 2091 video solution

video by Dr Chris Tisdell

$$-1/3 \leq x \leq 1$$

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$$|5-4x| > 2$$

Problem Statement

Find the values of $$x$$ that solve the inequality $$|5-4x| > 2$$

$$x < 3/4$$ or $$x > 7/4$$

Problem Statement

Find the values of $$x$$ that solve the inequality $$|5-4x| > 2$$

Solution

### Dr Chris Tisdell - 2092 video solution

video by Dr Chris Tisdell

$$x < 3/4$$ or $$x > 7/4$$

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$$3|x+7| > 27$$

Problem Statement

Find the values of $$x$$ that solve the inequality $$3|x+7| > 27$$.

Solution

### Freshmen Math Doctor - 2558 video solution

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$$|x+3| \leq 4$$

Problem Statement

Find the values of $$x$$ that solve the inequality $$|x+3| \leq 4$$.

Solution

### Freshmen Math Doctor - 2559 video solution

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$$|x| < 4$$

Problem Statement

Find the values of $$x$$ that solve $$|x| < 4$$.

$$-4 < x < 4$$

Problem Statement

Find the values of $$x$$ that solve $$|x| < 4$$.

Solution

### 2895 video solution

$$-4 < x < 4$$

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$$|2x - 3| \geq 8$$

Problem Statement

Find the values of $$x$$ that solve $$|2x - 3| \geq 8$$.

$$x \geq 5.5$$ or $$x \leq -2.5$$

Problem Statement

Find the values of $$x$$ that solve $$|2x - 3| \geq 8$$.

Solution

### 2896 video solution

$$x \geq 5.5$$ or $$x \leq -2.5$$

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$$5 - 3|4x+1| \geq -9$$

Problem Statement

Find the values of $$x$$ that solve $$5 - 3|4x+1| \geq -9$$.

$$-17/12 \leq x \leq 11/12$$

Problem Statement

Find the values of $$x$$ that solve $$5 - 3|4x+1| \geq -9$$.

Solution

### 2897 video solution

$$-17/12 \leq x \leq 11/12$$

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$$|2x + 5| > 11$$

Problem Statement

Find the values of $$x$$ that solve $$|2x + 5| > 11$$

$$x > 3$$ or $$x < -8$$

Problem Statement

Find the values of $$x$$ that solve $$|2x + 5| > 11$$

Solution

### 2898 video solution

$$x > 3$$ or $$x < -8$$

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$$|3x - 4| \leq 17$$

Problem Statement

Find the values of $$x$$ that solve $$|3x - 4| \leq 17$$.

$$13/3 \leq x \leq 7$$

Problem Statement

Find the values of $$x$$ that solve $$|3x - 4| \leq 17$$.

Solution

### 2899 video solution

$$13/3 \leq x \leq 7$$

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$$|3x + 5| \leq -3$$

Problem Statement

Find the values of $$x$$ that solve $$|3x + 5| \leq -3$$

no solution

Problem Statement

Find the values of $$x$$ that solve $$|3x + 5| \leq -3$$

Solution

### 2900 video solution

no solution

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$$|4x - 3| > -4$$

Problem Statement

Find the values of $$x$$ that solve $$|4x - 3| > -4$$

all real numbers

Problem Statement

Find the values of $$x$$ that solve $$|4x - 3| > -4$$

Solution

### 2901 video solution

all real numbers

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$$3|7x - 4| +5 > 17$$

Problem Statement

Find the values of $$x$$ that solve $$3|7x - 4| +5 > 17$$

$$x > 8/7$$ or $$x < 0$$

Problem Statement

Find the values of $$x$$ that solve $$3|7x - 4| +5 > 17$$

Solution

### 2902 video solution

$$x > 8/7$$ or $$x < 0$$

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$$2 \leq |3x+5| \leq 10$$

Problem Statement

Find the values of $$x$$ that solve $$2 \leq |3x+5| \leq 10$$ giving your answer in interval notation in exact form.

Solution

### Michael Penn - 3862 video solution

video by Michael Penn

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$$||3x-1|+4| \lt 8$$

Problem Statement

Find the values of $$x$$ that solve $$||3x-1|+4| \lt 8$$ giving your answer in interval notation in exact form.

Solution

### Michael Penn - 3863 video solution

video by Michael Penn

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