Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{+14}& = &8 \\\Leftrightarrow & 13x \color{red}{+14}\color{blue}{-14} & = &8\color{blue}{-14} \\\Leftrightarrow &13x & = &-6\\\Leftrightarrow & \color{red}{13}x & = &-6\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-6}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{+13}& = &10 \\\Leftrightarrow & 10x \color{red}{+13}\color{blue}{-13} & = &10\color{blue}{-13} \\\Leftrightarrow &10x & = &-3\\\Leftrightarrow & \color{red}{10}x & = &-3\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-3}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{10} } & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{+11}& = &6 \\\Leftrightarrow & -11x \color{red}{+11}\color{blue}{-11} & = &6\color{blue}{-11} \\\Leftrightarrow &-11x & = &-5\\\Leftrightarrow & \color{red}{-11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{+2}& = &3 \\\Leftrightarrow & 2x \color{red}{+2}\color{blue}{-2} & = &3\color{blue}{-2} \\\Leftrightarrow &2x & = &1\\\Leftrightarrow & \color{red}{2}x & = &1\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{1}{2} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{-9}& = &2 \\\Leftrightarrow & -2x \color{red}{-9}\color{blue}{+9} & = &2\color{blue}{+9} \\\Leftrightarrow &-2x & = &11\\\Leftrightarrow & \color{red}{-2}x & = &11\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{11}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{2} } & & \\ & V = \left\{ \frac{-11}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{+4}& = &14 \\\Leftrightarrow & -12x \color{red}{+4}\color{blue}{-4} & = &14\color{blue}{-4} \\\Leftrightarrow &-12x & = &10\\\Leftrightarrow & \color{red}{-12}x & = &10\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{10}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{-12}& = &-3 \\\Leftrightarrow & x \color{red}{-12}\color{blue}{+12} & = &-3\color{blue}{+12} \\\Leftrightarrow &x & = &9\\\Leftrightarrow & \color{red}{}x & = &9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 9 \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{-7}& = &-6 \\\Leftrightarrow & -11x \color{red}{-7}\color{blue}{+7} & = &-6\color{blue}{+7} \\\Leftrightarrow &-11x & = &1\\\Leftrightarrow & \color{red}{-11}x & = &1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{-1}& = &-12 \\\Leftrightarrow & -15x \color{red}{-1}\color{blue}{+1} & = &-12\color{blue}{+1} \\\Leftrightarrow &-15x & = &-11\\\Leftrightarrow & \color{red}{-15}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-11}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{11}{15} } & & \\ & V = \left\{ \frac{11}{15} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{-2}& = &-14 \\\Leftrightarrow & 6x \color{red}{-2}\color{blue}{+2} & = &-14\color{blue}{+2} \\\Leftrightarrow &6x & = &-12\\\Leftrightarrow & \color{red}{6}x & = &-12\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-12}{6} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{-8}& = &-3 \\\Leftrightarrow & -4x \color{red}{-8}\color{blue}{+8} & = &-3\color{blue}{+8} \\\Leftrightarrow &-4x & = &5\\\Leftrightarrow & \color{red}{-4}x & = &5\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{5}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{-1}& = &-1 \\\Leftrightarrow & 4x \color{red}{-1}\color{blue}{+1} & = &-1\color{blue}{+1} \\\Leftrightarrow &4x & = &0\\\Leftrightarrow & \color{red}{4}x & = &0\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{0}{4} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)