Practice Solutions

1. $–\frac{7}{3}x+\frac{21}{4}=\frac{3}{4}$

$\begin{array}{rcl}& & –\frac{21}{4} –\frac{21}{4}\\ –\frac{7}{3}x& =& –\frac{18}{4}\\ \left(\frac{–3}{7}\right)–\frac{7}{3}x& =& –\frac{9}{2}\left(\frac{–3}{7}\right)\\ x& =& \frac{27}{14}\end{array}$

2. $–4=4x+9$

$\begin{array}{rcl}& & –9 –9\\ \left(\frac{1}{4}\right)\left(–13\right)& =& 4x\left(\frac{1}{4}\right)\\ x& =& –\frac{13}{4}\end{array}$

3. $\frac{4}{5}x–7=5$

$\begin{array}{rcl}& & +7 +7\\ \left(\frac{5}{4}\right)\frac{4}{5}x& =& {}^3\cancel{12}\left(\frac{5}{{\cancel{4}}_1}\right)\\ x& =& 15\\ & & \end{array}$

4. $–\frac{31}{8}x=\frac{9}{2}$

$\begin{array}{rcl}\left(–\frac{8}{31}\right)–\frac{31}{8}x& =& \frac{9}{{}_1\cancel{2}}\left(–\frac{{\cancel{8}}^4}{31}\right)\\ x& =& –\frac{36}{31}\end{array}$

5. $\frac{5}{4}\left(x+16\right)=20$

$\begin{array}{rcl}\frac{5}{4}x+16\left(\frac{5}{4}\right)& =& 20\\ \frac{5}{4}x+20& =& 20\\ & & –20 –20\\ \left(\frac{4}{5}\right)\frac{5}{4}x& =& 0\left(\frac{4}{5}\right)\\ x& =& 0\end{array}$

6. $–\frac{1}{2}x+\frac{2}{3}=\frac{4}{3}$

$\begin{array}{rcl}& & –\frac{2}{3} –\frac{2}{3}\\ \left(\frac{–2}{1}\right)–\frac{1}{2}x& =& \frac{2}{3}\left(\frac{–2}{1}\right)\\ x& =& –\frac{4}{3}\end{array}$

7. $–\frac{3}{4}x+\frac{7}{8}=\frac{3}{8}$

$$\begin{gathered} –\frac{7}{8} –\frac{7}{8} \\ \left(–\frac{4}{3}\right)–\frac{3}{4}x=–\frac{4}{8}\left(–\frac{4}{3}\right) \\ x=–\frac{1}{{}_1\cancel{2}}\left(–\frac{{\cancel{4}}^2}{3}\right) \\ x=\frac{2}{3} \end{gathered}$$

8. $–\frac{1}{3}\left(8x–6\right)=6$

$$\begin{gathered} –\frac{8}{3}x–6\left(–\frac{1}{3}\right)=6 \\ –\frac{8}{3}x+2=6 \\ –2 –2 \\ \left(–\frac{3}{8}\right)\left(–\frac{8}{3}x\right)={}^1\cancel{4}\left(–\frac{3}{{\cancel{8}}_2}\right) \\ x=–\frac{3}{2} \end{gathered}$$

9. $\frac{x}{8}+3=–2$

$\begin{array}{rcl}& & –3 –3\\ \left(8\right)\frac{x}{8}& =& –5\left(8\right)\\ x& =& –40\end{array}$

10. $\frac{1}{3}\left(x–2\right)=4$

$\begin{array}{rcl}\frac{1}{3}x–\frac{2}{3}& =& 4\\ & & +\frac{2}{3} +\frac{2}{3}\\ \frac{1}{3}x& =& 4\frac{2}{3}\\ \left(\frac{3}{1}\right)\frac{1}{3}x& =& \frac{14}{3}\left(\frac{3}{1}\right) \\ x& =& 14\end{array}$

11. $\frac{9}{4}x–2=7$

$\begin{array}{rcl}& & \\ & & +2 +2\\ \left(\frac{4}{9}\right)\frac{9}{4}x& =& 9\left(\frac{4}{9}\right)\\ x& =& 4\end{array}$

12. $\frac{x}{5}–12=3$

$\begin{array}{rcl}& & +12 +12\\ \left(5\right)\frac{x}{5}& =& 15\left(5\right) \\ x& =& 75\end{array}$