Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{-9}& = &9 \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9} & = &9\color{blue}{+9} \\\Leftrightarrow &-5x & = &18\\\Leftrightarrow & \color{red}{-5}x & = &18\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{18}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{5} } & & \\ & V = \left\{ \frac{-18}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{-11}& = &5 \\\Leftrightarrow & -9x \color{red}{-11}\color{blue}{+11} & = &5\color{blue}{+11} \\\Leftrightarrow &-9x & = &16\\\Leftrightarrow & \color{red}{-9}x & = &16\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{16}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{9} } & & \\ & V = \left\{ \frac{-16}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{-12}& = &8 \\\Leftrightarrow & -3x \color{red}{-12}\color{blue}{+12} & = &8\color{blue}{+12} \\\Leftrightarrow &-3x & = &20\\\Leftrightarrow & \color{red}{-3}x & = &20\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{20}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{3} } & & \\ & V = \left\{ \frac{-20}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{-3}& = &6 \\\Leftrightarrow & -2x \color{red}{-3}\color{blue}{+3} & = &6\color{blue}{+3} \\\Leftrightarrow &-2x & = &9\\\Leftrightarrow & \color{red}{-2}x & = &9\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{9}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{2} } & & \\ & V = \left\{ \frac{-9}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{+9}& = &-11 \\\Leftrightarrow & x \color{red}{+9}\color{blue}{-9} & = &-11\color{blue}{-9} \\\Leftrightarrow &x & = &-20\\\Leftrightarrow & \color{red}{}x & = &-20\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -20 \\\Leftrightarrow & \color{green}{ x = -20 } & & \\ & V = \left\{ -20 \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{+6}& = &7 \\\Leftrightarrow & 8x \color{red}{+6}\color{blue}{-6} & = &7\color{blue}{-6} \\\Leftrightarrow &8x & = &1\\\Leftrightarrow & \color{red}{8}x & = &1\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{1}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{+11}& = &6 \\\Leftrightarrow & -10x \color{red}{+11}\color{blue}{-11} & = &6\color{blue}{-11} \\\Leftrightarrow &-10x & = &-5\\\Leftrightarrow & \color{red}{-10}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-5}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{+2}& = &4 \\\Leftrightarrow & -6x \color{red}{+2}\color{blue}{-2} & = &4\color{blue}{-2} \\\Leftrightarrow &-6x & = &2\\\Leftrightarrow & \color{red}{-6}x & = &2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{+10}& = &-8 \\\Leftrightarrow & 13x \color{red}{+10}\color{blue}{-10} & = &-8\color{blue}{-10} \\\Leftrightarrow &13x & = &-18\\\Leftrightarrow & \color{red}{13}x & = &-18\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-18}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{13} } & & \\ & V = \left\{ \frac{-18}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{+10}& = &-11 \\\Leftrightarrow & -3x \color{red}{+10}\color{blue}{-10} & = &-11\color{blue}{-10} \\\Leftrightarrow &-3x & = &-21\\\Leftrightarrow & \color{red}{-3}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-21}{-3} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{+1}& = &12 \\\Leftrightarrow & -9x \color{red}{+1}\color{blue}{-1} & = &12\color{blue}{-1} \\\Leftrightarrow &-9x & = &11\\\Leftrightarrow & \color{red}{-9}x & = &11\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{11}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{9} } & & \\ & V = \left\{ \frac{-11}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{-2}& = &-8 \\\Leftrightarrow & -6x \color{red}{-2}\color{blue}{+2} & = &-8\color{blue}{+2} \\\Leftrightarrow &-6x & = &-6\\\Leftrightarrow & \color{red}{-6}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-6}{-6} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)