1. Equations & Inequalities

Linear Inequalities

Textbook Question
Solve each absolute value inequality. 5|2x + 1| - 3 ≥ 9
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Textbook Question
In Exercises 59–94, solve each absolute value inequality. - 2|x - 4| ≥ - 4
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Textbook Question
Solve each absolute value inequality. - 4|1 - x| < - 16
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Textbook Question
To see how to solve an equation that involves the absolute value of a quadratic polynomial, such as | x^2 - x | = 6, work Exercises 83–86 in order. For x^2 - x to have an absolute value equal to 6, what are the two possible values that x may assume? (Hint: One is positive and the other is negative.)
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Textbook Question
Solve each inequality. Give the solution set using interval notation.
$11 x \geq 2 (x - 4)$
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Textbook Question
In Exercises 59–94, solve each absolute value inequality. 3 ≤ |2x - 1|
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Textbook Question
Solve each inequality. Give the solution set using interval notation. -5x - 4≥3(2x-5)
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Textbook Question
Solve each inequality. Give the solution set using interval notation.
$7 x - 2 (x - 3) \leq 5 (2 - x)$
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Textbook Question
Use the method described in Exercises 83–86, if applicable, and properties ofabsolute value to solve each equation or inequality. (Hint: Exercises 99 and 100 canbe solved by inspection.) | 3x^2 + x | = 14
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Textbook Question
Solve each inequality. Give the solution set using interval notation. 5 ≤ 2x -3 ≤ 7
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Textbook Question
In Exercises 59–94, solve each absolute value inequality. 5 > |4 - x|
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Textbook Question
Solve each inequality. Give the solution set using interval notation.
$- 8 > 3 x - 5 > - 12$
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Textbook Question
In Exercises 59–94, solve each absolute value inequality. 1 < |2 - 3x|
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Textbook Question
In Exercises 59–94, solve each absolute value inequality. $12 < \left| -2x + \frac{6}{7} \right| + \frac{3}{7}$
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Textbook Question
Solve each absolute value inequality. 4 + |3 - x/3| ≥ 9
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