Linear Equations with 1 Unknown Practice

\(5x – 2(7-x) = x+4 \\ \, \\ 5x \underbrace{-14 +2x}_{\text{Expand}} = x+4 \\ \, \\ \underbrace{(5x+2x)}_{\substack{\text{Combine} \\ \, \\ \text{Like-Terms}}} – 14 = x+4 \\ \, \\ 7x – 14 = x+4 \\ \, \\ 7x – 14 \color{red}{-x} = x+4 \color{red}{-x} \\ \, \\ 6x-14 = 4 \\ \, \\ 6x-14 \color{red}{+14} = 4 \color{red}{+14} \\ \, \\ 6x = 18 \\ \, \\ \dfrac{6x}{6} = \dfrac{18}{6} \\ \, \\ x = 3 \)

\(\require{cancel} 2(z+6) – 12 = 4(2z-12) \\ \, \\ \underbrace{2z+12}_{\text{Expand}} -12 = \underbrace{8z-48}_{\text{Expand}} \\ \, \\ 2z+ \cancelto{0}{{\color{red}{12-12}}} = 8z-48 \\ \, \\ 2z = 8z – 48 \\ \, \\ 2z \color{red}{+48} = 8z – 48 \color{red}{+48} \\ \, \\ 2z+48 = 8z \\ \, \\ 2z+48 \color{red}{-2z} = 8z \color{red}{-2z} \\ \, \\ 48 = 6z \\ \, \\ \dfrac{48}{\color{red}{6}} = \dfrac{6z}{\color{red}{6}} \\ \, \\ 8 = z \)

\(\require{cancel} \dfrac{8-6w}{5} = \dfrac{3}{10} + \dfrac{2w}{20} \\ \, \\ \text{Greatest Common Multiple}=20 \\ \, \\ \dfrac{8-6w}{5}\cdot\color{red}{20} = \dfrac{3}{10}\cdot\color{red}{20} + \dfrac{2w}{20}\cdot\color{red}{20} \\ \, \\ \dfrac{8-6w}{\cancel{5}}\cdot{\cancelto{4}{\color{red}{20}}} = \dfrac{3}{\cancel{10}}\cdot{\cancelto{2}{\color{red}{20}}} + \dfrac{2w}{\cancel{20}}\cdot{\cancel{\color{red}{20}}} \\ \, \\ (8-6w)4 = 3 \cdot 2 + 2w \\ \, \\ 32 – 24w = 6 + 2w \\ \, \\ 32 – 24w {\color{red}{+24w}} = 6 + 2w {\color{red}{+24w}} \\ \, \\ 32 = 6 + 26w \\ \, \\ 32 {\color{red}{-6}}= 6 + 26w {\color{red}{-6}} \\ \, \\ 26 = 26w \\ \, \\ \dfrac{26}{{\color{red}{26}}} = \dfrac{26w}{{\color{red}{26}}} \\ \, \\ 1 = w \)