Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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