Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{+5}& = &4 \\\Leftrightarrow & -14x \color{red}{+5}\color{blue}{-5} & = &4\color{blue}{-5} \\\Leftrightarrow &-14x & = &-1\\\Leftrightarrow & \color{red}{-14}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-1}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{14} } & & \\ & V = \left\{ \frac{1}{14} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{+8}& = &14 \\\Leftrightarrow & 8x \color{red}{+8}\color{blue}{-8} & = &14\color{blue}{-8} \\\Leftrightarrow &8x & = &6\\\Leftrightarrow & \color{red}{8}x & = &6\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{6}{8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{-1}& = &-1 \\\Leftrightarrow & 12x \color{red}{-1}\color{blue}{+1} & = &-1\color{blue}{+1} \\\Leftrightarrow &12x & = &0\\\Leftrightarrow & \color{red}{12}x & = &0\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{0}{12} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{-3}& = &-3 \\\Leftrightarrow & -14x \color{red}{-3}\color{blue}{+3} & = &-3\color{blue}{+3} \\\Leftrightarrow &-14x & = &0\\\Leftrightarrow & \color{red}{-14}x & = &0\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{0}{-14} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{-8}& = &10 \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8} & = &10\color{blue}{+8} \\\Leftrightarrow &14x & = &18\\\Leftrightarrow & \color{red}{14}x & = &18\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{18}{14} \\\Leftrightarrow & \color{green}{ x = \frac{9}{7} } & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{-8}& = &5 \\\Leftrightarrow & 3x \color{red}{-8}\color{blue}{+8} & = &5\color{blue}{+8} \\\Leftrightarrow &3x & = &13\\\Leftrightarrow & \color{red}{3}x & = &13\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{13}{3} \\\Leftrightarrow & \color{green}{ x = \frac{13}{3} } & & \\ & V = \left\{ \frac{13}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{-3}& = &-5 \\\Leftrightarrow & x \color{red}{-3}\color{blue}{+3} & = &-5\color{blue}{+3} \\\Leftrightarrow &x & = &-2\\\Leftrightarrow & \color{red}{}x & = &-2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -2 \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{-2}& = &-7 \\\Leftrightarrow & 9x \color{red}{-2}\color{blue}{+2} & = &-7\color{blue}{+2} \\\Leftrightarrow &9x & = &-5\\\Leftrightarrow & \color{red}{9}x & = &-5\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-5}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{9} } & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{+8}& = &3 \\\Leftrightarrow & 9x \color{red}{+8}\color{blue}{-8} & = &3\color{blue}{-8} \\\Leftrightarrow &9x & = &-5\\\Leftrightarrow & \color{red}{9}x & = &-5\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-5}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{9} } & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & x \color{red}{+14}& = &14 \\\Leftrightarrow & x \color{red}{+14}\color{blue}{-14} & = &14\color{blue}{-14} \\\Leftrightarrow &x & = &0\\\Leftrightarrow & \color{red}{}x & = &0\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 0 \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{-13}& = &8 \\\Leftrightarrow & -3x \color{red}{-13}\color{blue}{+13} & = &8\color{blue}{+13} \\\Leftrightarrow &-3x & = &21\\\Leftrightarrow & \color{red}{-3}x & = &21\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{21}{-3} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{+7}& = &13 \\\Leftrightarrow & -10x \color{red}{+7}\color{blue}{-7} & = &13\color{blue}{-7} \\\Leftrightarrow &-10x & = &6\\\Leftrightarrow & \color{red}{-10}x & = &6\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{6}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)