Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & x \color{red}{-1}& = &14 \\\Leftrightarrow & x \color{red}{-1}\color{blue}{+1} & = &14\color{blue}{+1} \\\Leftrightarrow &x & = &15\\\Leftrightarrow & \color{red}{}x & = &15\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 15 \\\Leftrightarrow & \color{green}{ x = 15 } & & \\ & V = \left\{ 15 \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{+9}& = &-7 \\\Leftrightarrow & 14x \color{red}{+9}\color{blue}{-9} & = &-7\color{blue}{-9} \\\Leftrightarrow &14x & = &-16\\\Leftrightarrow & \color{red}{14}x & = &-16\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-16}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{+1}& = &-12 \\\Leftrightarrow & -3x \color{red}{+1}\color{blue}{-1} & = &-12\color{blue}{-1} \\\Leftrightarrow &-3x & = &-13\\\Leftrightarrow & \color{red}{-3}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-13}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{13}{3} } & & \\ & V = \left\{ \frac{13}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{-15}& = &1 \\\Leftrightarrow & -10x \color{red}{-15}\color{blue}{+15} & = &1\color{blue}{+15} \\\Leftrightarrow &-10x & = &16\\\Leftrightarrow & \color{red}{-10}x & = &16\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{16}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{+6}& = &15 \\\Leftrightarrow & -13x \color{red}{+6}\color{blue}{-6} & = &15\color{blue}{-6} \\\Leftrightarrow &-13x & = &9\\\Leftrightarrow & \color{red}{-13}x & = &9\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{9}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{13} } & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{+13}& = &-14 \\\Leftrightarrow & -8x \color{red}{+13}\color{blue}{-13} & = &-14\color{blue}{-13} \\\Leftrightarrow &-8x & = &-27\\\Leftrightarrow & \color{red}{-8}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-27}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{27}{8} } & & \\ & V = \left\{ \frac{27}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{-2}& = &-2 \\\Leftrightarrow & 12x \color{red}{-2}\color{blue}{+2} & = &-2\color{blue}{+2} \\\Leftrightarrow &12x & = &0\\\Leftrightarrow & \color{red}{12}x & = &0\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{0}{12} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{-9}& = &-2 \\\Leftrightarrow & -14x \color{red}{-9}\color{blue}{+9} & = &-2\color{blue}{+9} \\\Leftrightarrow &-14x & = &7\\\Leftrightarrow & \color{red}{-14}x & = &7\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{7}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{-14}& = &11 \\\Leftrightarrow & 3x \color{red}{-14}\color{blue}{+14} & = &11\color{blue}{+14} \\\Leftrightarrow &3x & = &25\\\Leftrightarrow & \color{red}{3}x & = &25\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{25}{3} \\\Leftrightarrow & \color{green}{ x = \frac{25}{3} } & & \\ & V = \left\{ \frac{25}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{-11}& = &-11 \\\Leftrightarrow & 3x \color{red}{-11}\color{blue}{+11} & = &-11\color{blue}{+11} \\\Leftrightarrow &3x & = &0\\\Leftrightarrow & \color{red}{3}x & = &0\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{0}{3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{-14}& = &9 \\\Leftrightarrow & 5x \color{red}{-14}\color{blue}{+14} & = &9\color{blue}{+14} \\\Leftrightarrow &5x & = &23\\\Leftrightarrow & \color{red}{5}x & = &23\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{23}{5} \\\Leftrightarrow & \color{green}{ x = \frac{23}{5} } & & \\ & V = \left\{ \frac{23}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{+10}& = &-2 \\\Leftrightarrow & 10x \color{red}{+10}\color{blue}{-10} & = &-2\color{blue}{-10} \\\Leftrightarrow &10x & = &-12\\\Leftrightarrow & \color{red}{10}x & = &-12\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-12}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)