Basic Solving Practice
- Page ID
- 160082
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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 for \(x\).
1. \( 2x + 3 = 7 \)
2. \( 4x - 5 = 15 \)
3. \( \frac{3x}{2} + 4 = 10 \)
4. \( 5x - 2 = 3x + 6 \)
5. \( 7 - x = 2x + 8 \)
6. \( \frac{x - 1}{3} = 2 \)
7. \( 6x + 5 = 2x + 17 \)
8. \( 3(x - 4) = 2x + 1 \)
9. \( 2(x + 3) - 4 = 10 \)
10. \( \frac{5x + 2}{4} = 3 \)
11. \( 8 - \frac{x}{2} = 3 \)
12. \( 4x + 7 = 3(x - 2) \)
13. \( 2(x + 5) = 3x - 4 \)
14. \( \frac{2x - 3}{5} = \frac{x + 1}{2} \)
15. \( 6x - 8 = 4x + 10 \)
16. \( \frac{3x + 4}{2} - 5 = 7 \)
17. \( 9 - \frac{2x}{3} = 1 \)
18. \( 4(x - 2) + 3 = 5x - 1 \)
19. \( \frac{5x + 3}{3} = 2x + 1 \)
20. \( 7x - 4 = 3x + 12 \)
Solve the quadratic equations.
1. \(x^2 - 5x + 6 = 0\)
2. \(x^2 + 4x - 12 = 0\)
3. \(2x^2 - 8x + 6 = 0\)
4. \(x^2 - 9 = 0\)
5. \(3x^2 + 2x - 8 = 0\)
6. \(x^2 + 6x + 9 = 0\)
7. \(4x^2 - 4x - 8 = 0\)
8. \(x^2 - 4x - 5 = 0\)
9. \(2x^2 + 3x - 2 = 0\)
10. \(x^2 - 2x - 15 = 0\)
11. \(x^2 + 2x - 35 = 0\)
12. \(3x^2 - 14x + 8 = 0\)
13. \(5x^2 - 20 = 0\)
14. \(x^2 + 8x + 16 = 0\)
15. \(2x^2 - 5x + 3 = 0\)
16. \(x^2 - 6x + 8 = 0\)
17. \(4x^2 + 7x - 2 = 0\)
18. \(x^2 - 3x - 10 = 0\)
19. \(3x^2 + x - 4 = 0\)
20. \(x^2 + 5x + 6 = 0\)
Solve the absolute value equations.
1. \(|x - 3| = 7\)
2. \(|2x + 1| = 5\)
3. \(|x + 4| = 9\)
4. \(|3x - 2| = 4\)
5. \(|x - 5| = 3x - 7\)
6. \(|2x - 1| = 6\)
7. \(|x + 2| = |x - 4|\)
8. \(|x - 1| = 2x + 3\)
9. \(|x + 5| = 2x - 1\)
10. \(|3x + 4| = |x - 2|\)