Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{+13}& = &14 \\\Leftrightarrow & 9x \color{red}{+13}\color{blue}{-13} & = &14\color{blue}{-13} \\\Leftrightarrow &9x & = &1\\\Leftrightarrow & \color{red}{9}x & = &1\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{1}{9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{+14}& = &14 \\\Leftrightarrow & 2x \color{red}{+14}\color{blue}{-14} & = &14\color{blue}{-14} \\\Leftrightarrow &2x & = &0\\\Leftrightarrow & \color{red}{2}x & = &0\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{0}{2} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{+11}& = &-8 \\\Leftrightarrow & -15x \color{red}{+11}\color{blue}{-11} & = &-8\color{blue}{-11} \\\Leftrightarrow &-15x & = &-19\\\Leftrightarrow & \color{red}{-15}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-19}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{19}{15} } & & \\ & V = \left\{ \frac{19}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{+10}& = &10 \\\Leftrightarrow & 9x \color{red}{+10}\color{blue}{-10} & = &10\color{blue}{-10} \\\Leftrightarrow &9x & = &0\\\Leftrightarrow & \color{red}{9}x & = &0\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{0}{9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{-11}& = &5 \\\Leftrightarrow & 6x \color{red}{-11}\color{blue}{+11} & = &5\color{blue}{+11} \\\Leftrightarrow &6x & = &16\\\Leftrightarrow & \color{red}{6}x & = &16\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{16}{6} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{-11}& = &1 \\\Leftrightarrow & 6x \color{red}{-11}\color{blue}{+11} & = &1\color{blue}{+11} \\\Leftrightarrow &6x & = &12\\\Leftrightarrow & \color{red}{6}x & = &12\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{12}{6} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{+2}& = &7 \\\Leftrightarrow & -6x \color{red}{+2}\color{blue}{-2} & = &7\color{blue}{-2} \\\Leftrightarrow &-6x & = &5\\\Leftrightarrow & \color{red}{-6}x & = &5\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{5}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{-3}& = &11 \\\Leftrightarrow & -10x \color{red}{-3}\color{blue}{+3} & = &11\color{blue}{+3} \\\Leftrightarrow &-10x & = &14\\\Leftrightarrow & \color{red}{-10}x & = &14\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{14}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{-4}& = &-14 \\\Leftrightarrow & 2x \color{red}{-4}\color{blue}{+4} & = &-14\color{blue}{+4} \\\Leftrightarrow &2x & = &-10\\\Leftrightarrow & \color{red}{2}x & = &-10\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-10}{2} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{+11}& = &-5 \\\Leftrightarrow & -2x \color{red}{+11}\color{blue}{-11} & = &-5\color{blue}{-11} \\\Leftrightarrow &-2x & = &-16\\\Leftrightarrow & \color{red}{-2}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-16}{-2} \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{-13}& = &-1 \\\Leftrightarrow & 12x \color{red}{-13}\color{blue}{+13} & = &-1\color{blue}{+13} \\\Leftrightarrow &12x & = &12\\\Leftrightarrow & \color{red}{12}x & = &12\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{12}{12} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{-3}& = &-8 \\\Leftrightarrow & 11x \color{red}{-3}\color{blue}{+3} & = &-8\color{blue}{+3} \\\Leftrightarrow &11x & = &-5\\\Leftrightarrow & \color{red}{11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)