Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{-7}& = &-15 \\\Leftrightarrow & 5x \color{red}{-7}\color{blue}{+7} & = &-15\color{blue}{+7} \\\Leftrightarrow &5x & = &-8\\\Leftrightarrow & \color{red}{5}x & = &-8\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-8}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{+13}& = &5 \\\Leftrightarrow & -3x \color{red}{+13}\color{blue}{-13} & = &5\color{blue}{-13} \\\Leftrightarrow &-3x & = &-8\\\Leftrightarrow & \color{red}{-3}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{+11}& = &-3 \\\Leftrightarrow & 3x \color{red}{+11}\color{blue}{-11} & = &-3\color{blue}{-11} \\\Leftrightarrow &3x & = &-14\\\Leftrightarrow & \color{red}{3}x & = &-14\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-14}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{3} } & & \\ & V = \left\{ \frac{-14}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{-14}& = &2 \\\Leftrightarrow & 5x \color{red}{-14}\color{blue}{+14} & = &2\color{blue}{+14} \\\Leftrightarrow &5x & = &16\\\Leftrightarrow & \color{red}{5}x & = &16\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{16}{5} \\\Leftrightarrow & \color{green}{ x = \frac{16}{5} } & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{+4}& = &10 \\\Leftrightarrow & 12x \color{red}{+4}\color{blue}{-4} & = &10\color{blue}{-4} \\\Leftrightarrow &12x & = &6\\\Leftrightarrow & \color{red}{12}x & = &6\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{6}{12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{+5}& = &-13 \\\Leftrightarrow & -15x \color{red}{+5}\color{blue}{-5} & = &-13\color{blue}{-5} \\\Leftrightarrow &-15x & = &-18\\\Leftrightarrow & \color{red}{-15}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-18}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{-12}& = &5 \\\Leftrightarrow & -14x \color{red}{-12}\color{blue}{+12} & = &5\color{blue}{+12} \\\Leftrightarrow &-14x & = &17\\\Leftrightarrow & \color{red}{-14}x & = &17\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{17}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{14} } & & \\ & V = \left\{ \frac{-17}{14} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{-13}& = &-13 \\\Leftrightarrow & 3x \color{red}{-13}\color{blue}{+13} & = &-13\color{blue}{+13} \\\Leftrightarrow &3x & = &0\\\Leftrightarrow & \color{red}{3}x & = &0\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{0}{3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{+6}& = &-10 \\\Leftrightarrow & -4x \color{red}{+6}\color{blue}{-6} & = &-10\color{blue}{-6} \\\Leftrightarrow &-4x & = &-16\\\Leftrightarrow & \color{red}{-4}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-16}{-4} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
10. \(\begin{align} & x \color{red}{-14}& = &7 \\\Leftrightarrow & x \color{red}{-14}\color{blue}{+14} & = &7\color{blue}{+14} \\\Leftrightarrow &x & = &21\\\Leftrightarrow & \color{red}{}x & = &21\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 21 \\\Leftrightarrow & \color{green}{ x = 21 } & & \\ & V = \left\{ 21 \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{+10}& = &-1 \\\Leftrightarrow & -8x \color{red}{+10}\color{blue}{-10} & = &-1\color{blue}{-10} \\\Leftrightarrow &-8x & = &-11\\\Leftrightarrow & \color{red}{-8}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-11}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{11}{8} } & & \\ & V = \left\{ \frac{11}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{+4}& = &11 \\\Leftrightarrow & 12x \color{red}{+4}\color{blue}{-4} & = &11\color{blue}{-4} \\\Leftrightarrow &12x & = &7\\\Leftrightarrow & \color{red}{12}x & = &7\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{7}{12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{12} } & & \\ & V = \left\{ \frac{7}{12} \right\} & \\\end{align}\)