Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{+7}& = &4 \\\Leftrightarrow & -8x \color{red}{+7}\color{blue}{-7} & = &4\color{blue}{-7} \\\Leftrightarrow &-8x & = &-3\\\Leftrightarrow & \color{red}{-8}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-3}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{-6}& = &-14 \\\Leftrightarrow & 11x \color{red}{-6}\color{blue}{+6} & = &-14\color{blue}{+6} \\\Leftrightarrow &11x & = &-8\\\Leftrightarrow & \color{red}{11}x & = &-8\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-8}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{11} } & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{+9}& = &12 \\\Leftrightarrow & -13x \color{red}{+9}\color{blue}{-9} & = &12\color{blue}{-9} \\\Leftrightarrow &-13x & = &3\\\Leftrightarrow & \color{red}{-13}x & = &3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{-11}& = &-13 \\\Leftrightarrow & 5x \color{red}{-11}\color{blue}{+11} & = &-13\color{blue}{+11} \\\Leftrightarrow &5x & = &-2\\\Leftrightarrow & \color{red}{5}x & = &-2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{-11}& = &12 \\\Leftrightarrow & 10x \color{red}{-11}\color{blue}{+11} & = &12\color{blue}{+11} \\\Leftrightarrow &10x & = &23\\\Leftrightarrow & \color{red}{10}x & = &23\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{23}{10} \\\Leftrightarrow & \color{green}{ x = \frac{23}{10} } & & \\ & V = \left\{ \frac{23}{10} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{+12}& = &7 \\\Leftrightarrow & -14x \color{red}{+12}\color{blue}{-12} & = &7\color{blue}{-12} \\\Leftrightarrow &-14x & = &-5\\\Leftrightarrow & \color{red}{-14}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-5}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{14} } & & \\ & V = \left\{ \frac{5}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{+7}& = &3 \\\Leftrightarrow & -15x \color{red}{+7}\color{blue}{-7} & = &3\color{blue}{-7} \\\Leftrightarrow &-15x & = &-4\\\Leftrightarrow & \color{red}{-15}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{15} } & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{+5}& = &3 \\\Leftrightarrow & x \color{red}{+5}\color{blue}{-5} & = &3\color{blue}{-5} \\\Leftrightarrow &x & = &-2\\\Leftrightarrow & \color{red}{}x & = &-2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -2 \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{-15}& = &-8 \\\Leftrightarrow & 6x \color{red}{-15}\color{blue}{+15} & = &-8\color{blue}{+15} \\\Leftrightarrow &6x & = &7\\\Leftrightarrow & \color{red}{6}x & = &7\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{7}{6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{6} } & & \\ & V = \left\{ \frac{7}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{+8}& = &-3 \\\Leftrightarrow & 9x \color{red}{+8}\color{blue}{-8} & = &-3\color{blue}{-8} \\\Leftrightarrow &9x & = &-11\\\Leftrightarrow & \color{red}{9}x & = &-11\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-11}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{9} } & & \\ & V = \left\{ \frac{-11}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{+14}& = &-5 \\\Leftrightarrow & -8x \color{red}{+14}\color{blue}{-14} & = &-5\color{blue}{-14} \\\Leftrightarrow &-8x & = &-19\\\Leftrightarrow & \color{red}{-8}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-19}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{19}{8} } & & \\ & V = \left\{ \frac{19}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{+8}& = &7 \\\Leftrightarrow & 10x \color{red}{+8}\color{blue}{-8} & = &7\color{blue}{-8} \\\Leftrightarrow &10x & = &-1\\\Leftrightarrow & \color{red}{10}x & = &-1\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-1}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)