Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

1. \(-7x-2=-1\)
2. \(8x-10=5\)
3. \(-15x+14=15\)
4. \(10x+4=10\)
5. \(15x-11=-8\)
6. \(-13x-15=4\)
7. \(-13x-1=7\)
8. \(x+2=-15\)
9. \(13x+6=-3\)
10. \(-8x-11=-8\)
11. \(10x-13=1\)
12. \(5x-1=-11\)

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{-2}& = &-1 \\\Leftrightarrow & -7x \color{red}{-2}\color{blue}{+2} & = &-1\color{blue}{+2} \\\Leftrightarrow &-7x & = &1\\\Leftrightarrow & \color{red}{-7}x & = &1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{-10}& = &5 \\\Leftrightarrow & 8x \color{red}{-10}\color{blue}{+10} & = &5\color{blue}{+10} \\\Leftrightarrow &8x & = &15\\\Leftrightarrow & \color{red}{8}x & = &15\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{15}{8} \\\Leftrightarrow & \color{green}{ x = \frac{15}{8} } & & \\ & V = \left\{ \frac{15}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{+14}& = &15 \\\Leftrightarrow & -15x \color{red}{+14}\color{blue}{-14} & = &15\color{blue}{-14} \\\Leftrightarrow &-15x & = &1\\\Leftrightarrow & \color{red}{-15}x & = &1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{15} } & & \\ & V = \left\{ \frac{-1}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{+4}& = &10 \\\Leftrightarrow & 10x \color{red}{+4}\color{blue}{-4} & = &10\color{blue}{-4} \\\Leftrightarrow &10x & = &6\\\Leftrightarrow & \color{red}{10}x & = &6\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{6}{10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{-11}& = &-8 \\\Leftrightarrow & 15x \color{red}{-11}\color{blue}{+11} & = &-8\color{blue}{+11} \\\Leftrightarrow &15x & = &3\\\Leftrightarrow & \color{red}{15}x & = &3\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{3}{15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{-15}& = &4 \\\Leftrightarrow & -13x \color{red}{-15}\color{blue}{+15} & = &4\color{blue}{+15} \\\Leftrightarrow &-13x & = &19\\\Leftrightarrow & \color{red}{-13}x & = &19\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{19}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{13} } & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{-1}& = &7 \\\Leftrightarrow & -13x \color{red}{-1}\color{blue}{+1} & = &7\color{blue}{+1} \\\Leftrightarrow &-13x & = &8\\\Leftrightarrow & \color{red}{-13}x & = &8\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{8}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{13} } & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{+2}& = &-15 \\\Leftrightarrow & x \color{red}{+2}\color{blue}{-2} & = &-15\color{blue}{-2} \\\Leftrightarrow &x & = &-17\\\Leftrightarrow & \color{red}{}x & = &-17\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -17 \\\Leftrightarrow & \color{green}{ x = -17 } & & \\ & V = \left\{ -17 \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{+6}& = &-3 \\\Leftrightarrow & 13x \color{red}{+6}\color{blue}{-6} & = &-3\color{blue}{-6} \\\Leftrightarrow &13x & = &-9\\\Leftrightarrow & \color{red}{13}x & = &-9\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-9}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{13} } & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{-11}& = &-8 \\\Leftrightarrow & -8x \color{red}{-11}\color{blue}{+11} & = &-8\color{blue}{+11} \\\Leftrightarrow &-8x & = &3\\\Leftrightarrow & \color{red}{-8}x & = &3\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{3}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{-13}& = &1 \\\Leftrightarrow & 10x \color{red}{-13}\color{blue}{+13} & = &1\color{blue}{+13} \\\Leftrightarrow &10x & = &14\\\Leftrightarrow & \color{red}{10}x & = &14\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{14}{10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{-1}& = &-11 \\\Leftrightarrow & 5x \color{red}{-1}\color{blue}{+1} & = &-11\color{blue}{+1} \\\Leftrightarrow &5x & = &-10\\\Leftrightarrow & \color{red}{5}x & = &-10\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-10}{5} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)