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Section 5.1 Equations and Inequalities
Checkpoint 5.1.1.
Solve by factorization:
\(x^2 - 5x + 6 = 0\)
Checkpoint 5.1.2.
Solve by factorization:
\(x^2 + 7x + 12 = 0\)
Checkpoint 5.1.3.
Solve by factorization:
\(2x^2 - 7x + 3 = 0\)
Checkpoint 5.1.4.
Solve by factorization:
\(x^2 - 16 = 0\)
Checkpoint 5.1.5.
Solve by factorization:
\(3x^2 - 12x = 0\)
Checkpoint 5.1.6.
Solve by factorization:
\(x^2 + 5x - 14 = 0\)
Checkpoint 5.1.7.
Solve by factorization:
\(4x^2 - 25 = 0\)
\(x = -\frac{5}{2}, \frac{5}{2}\)
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Checkpoint 5.1.8.
Solve by factorization:
\(6x^2 + x - 12 = 0\)
\(x = -\frac{3}{2}, \frac{4}{3}\)
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Checkpoint 5.1.9.
Solve by factorization:
\(x^2 - 8x + 15 = 0\)
Checkpoint 5.1.10.
First bring to standard form, then solve by factorization:
\(x^2 + 9 = 6x\)
Checkpoint 5.1.11.
Solve for x: \(5x - 5 \lt 10\)
Checkpoint 5.1.12.
Solve for x: \(-2x + 6 \gt 12\)
Checkpoint 5.1.13.
Solve for x: \(-\frac{2}{x+3} \gt \frac{5}{x-3}\)
\(x \in (-\infty, -3) \cup (-9/7, 3)\)
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Checkpoint 5.1.14.
Solve for x: \(\frac{x}{x-1} \lt 0\)
\(x \in [0, 1) \) or \(0 \le x \lt 1\)
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\(x \in (0, 1)\) or \(0 \lt x \lt 1\)
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\(x \in [0, 1]\) or \(0 \le x \le 1\)
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Checkpoint 5.1.15.
Solve for x: \((x - 1)(x - 4) \lt 0\)
Checkpoint 5.1.16.
Solve for x: \((x - 3)(x - 5) \gt 0\)
\(x \in (-\infty, 3) \cup (5, \infty)\)
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\(x \in (\infty, 3) \cup (5, -\infty)\)
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\(x \in [-\infty, 3) \cup (5, \infty]\)
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Checkpoint 5.1.17.
Solve for x: \((3x - 2)(x - 5) \le 0\)
\(x \in (\frac{2}{3}, 5)\)
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\(x \in [\frac{2}{3}, 5]\)
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\(x \in (\frac{2}{3}, 5]\)
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Checkpoint 5.1.18.
Solve for x: \((x - 1)(x - 3)(x + 5) \le 0\)
\(x \in (-\infty, -5) \cup [3, 1]\)
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\(x \in (-\infty, -5] \cup (3, 1)\)
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\(x \in (-\infty, -5] \cup [1, 3]\)
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Checkpoint 5.1.19.
Solve for x: \(\frac{(x - 1)(x + 5)}{(x - 3)} \le 0\)
\(x \in (-\infty, -5] \cup [1, 3)\)
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\(x \in (-\infty, -5] \cup [1, 3]\)
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\(x \in (-\infty, -5) \cup [1, 3)\)
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Checkpoint 5.1.20.
Solve for x: \(\frac{(x - 1)(x + 5)}{(x - 3)} \ge 0\)
\(x \in (-5, 1) \cup [3, \infty)\)
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\(x \in [-5, 1] \cup (3, \infty)\)
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\(x \in (-\infty, 1] \cup [3, \infty)\)
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Checkpoint 5.1.21.
Show your work and solve for x: \(\frac{(2 - x^2)(x - 3)}{x^2 - 3x - 4} \ge 0\)
Answer.
This is an open-ended question. Students should show all work including sign chart / critical points / test intervals.
Solving Absolute Value Equations and Inequalities
Checkpoint 5.1.22.
Solve for
\(x\) given the equation
\(|x| = 12\text{.}\)
\(x = 12\) or
\(\, x = -12\)
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Checkpoint 5.1.23.
What is the value of
\(x\) in the equation
\(|10 - 5x| = 0\text{?}\)
Checkpoint 5.1.24.
Solve the equation
\(|x - 4| = 7\text{.}\)
Checkpoint 5.1.25.
Find the solution to
\(|2x + 5| = - 4\text{.}\)
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\(x = -4.5\) or
\(x = -0.5\)
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Checkpoint 5.1.26.
Solve the inequality
\(|x| \gt 5\text{.}\)
\(x > 5\) or
\(x \lt -5\)
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\(x \geq 5\) or
\(x \leq -5\)
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Checkpoint 5.1.27.
What is the solution to the inequality
\(|x| \leq 2\text{?}\)
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\(x \leq 2\) or
\(x \geq -2\)
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Checkpoint 5.1.28.
Solve the inequality
\(|x + 2| \lt 3\text{.}\)
Checkpoint 5.1.29.
Find the solution to the inequality
\(|3x + 4| \geq 2\text{.}\)
\(x \geq -\frac{2}{3} \) or
\(x \leq -2\)
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\(-\frac{4}{3} \leq x \leq 2\)
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\(x \leq -\frac{4}{3}\) only
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Checkpoint 5.1.30.
Solve the inequality
\(|x - 5| \leq 1\text{.}\)
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\(x \leq 6\) or,
\(x \geq 4\)
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Checkpoint 5.1.31.
What is the solution to the equation
\(|x^2 - 9| = 0\text{?}\)
