3.2E Exercises
- Page ID
- 152974
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Solve the inequalities.
- \( 14x + 32 < 4 \)
- \( \frac{3}{2} x + 6 > 0 \)
- \( 6q + 2 \geq 4q - 3 \)
- \( 2x - 1 \leq 12 \)
- \( 5 - 3x > -4 \)
- \( -4x + \frac{1}{2} \leq 0 \)
- \( ax + b \leq c \), where \(a, b,\) and \(c\) are constants, and \(a > 0\)
- \( ax + b \leq c \), where \(a, b,\) and \(c\) are constants, and \(a < 0\)
- Answer
-
- \( x < -2\) or \( (-\infty, 2)\)
- \( x > -4\) or \( (-4, \infty) \)
- \( q \geq -\frac{5}{2} \) or \( \left[ -\frac{5}{2}, \infty \right) \)
- \( x \leq \frac{13}{2} \) or \( \left( -\infty, \frac{13}{2} \right] \)
- \( x< 3 \)
- \( x \geq \frac{1}{8} \)
- \( x \leq \frac{c-b}{a} \)
- \(x \geq \frac{c-b}{a} \)
Solve the inequalities.
1. \( x^2 \geq 4 \)
2. \( x^4 \geq 16 \)
3. \( x^2 +3x < -2 \)
4. \( x^2 - 5x +6 < 0 \)
5. \( \dfrac{x}{x+2} \leq 0 \)
6. \( \dfrac{2}{x+3} \leq 0 \)
- Answer
-
- \( x \geq 2 \) or \( x \leq -2 \), or \( (-\infty, -2] \cup [2, \infty) \)
- \( x \geq 2 \) or \( x \leq -2 \), or \( (-\infty, -2] \cup [2, \infty) \)
- \( -2 < x < -1 \), or \( (-2, -1) \)
- \( 2 < x < 3 \), or \( (2, 3) \)
- \( -2 < x \leq 0 \), or \( (-2, 0]\)
- \( x < -3\), or \( (-\infty, -3) \)
Solve the inequalities.
- \( -1 \leq 3x + 4 \leq 1 \)
- \( |2x + 8 | < 2 \)
- \( \left| \dfrac{x+1}{2} \right| \geq 3 \)
- \( |3 - x| > 9 \)
- Answer
-
- \( -\frac{5}{3} \leq x \leq -1 \), or \( \left[ -\frac{5}{3}, -1 \right] \)
- \( -5 < x < -3 \), or \( (-5, -3) \)
- \( x \leq -7 \) or \(x \geq 5 \), or \( (-\infty, -7] \cup [5, \infty) \)
- \( x < -6\) or \(x > 12 \), or \( (-\infty, -6) \cup (12, \infty) \)