Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{+14}& = &10 \\\Leftrightarrow & -4x \color{red}{+14}\color{blue}{-14} & = &10\color{blue}{-14} \\\Leftrightarrow &-4x & = &-4\\\Leftrightarrow & \color{red}{-4}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-4}{-4} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{-15}& = &3 \\\Leftrightarrow & -15x \color{red}{-15}\color{blue}{+15} & = &3\color{blue}{+15} \\\Leftrightarrow &-15x & = &18\\\Leftrightarrow & \color{red}{-15}x & = &18\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{18}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{+15}& = &3 \\\Leftrightarrow & 9x \color{red}{+15}\color{blue}{-15} & = &3\color{blue}{-15} \\\Leftrightarrow &9x & = &-12\\\Leftrightarrow & \color{red}{9}x & = &-12\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-12}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{+12}& = &-14 \\\Leftrightarrow & 6x \color{red}{+12}\color{blue}{-12} & = &-14\color{blue}{-12} \\\Leftrightarrow &6x & = &-26\\\Leftrightarrow & \color{red}{6}x & = &-26\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-26}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{3} } & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{+4}& = &-8 \\\Leftrightarrow & 12x \color{red}{+4}\color{blue}{-4} & = &-8\color{blue}{-4} \\\Leftrightarrow &12x & = &-12\\\Leftrightarrow & \color{red}{12}x & = &-12\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-12}{12} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{-14}& = &-13 \\\Leftrightarrow & 10x \color{red}{-14}\color{blue}{+14} & = &-13\color{blue}{+14} \\\Leftrightarrow &10x & = &1\\\Leftrightarrow & \color{red}{10}x & = &1\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{1}{10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{10} } & & \\ & V = \left\{ \frac{1}{10} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{-8}& = &11 \\\Leftrightarrow & x \color{red}{-8}\color{blue}{+8} & = &11\color{blue}{+8} \\\Leftrightarrow &x & = &19\\\Leftrightarrow & \color{red}{}x & = &19\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 19 \\\Leftrightarrow & \color{green}{ x = 19 } & & \\ & V = \left\{ 19 \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{+12}& = &-12 \\\Leftrightarrow & -4x \color{red}{+12}\color{blue}{-12} & = &-12\color{blue}{-12} \\\Leftrightarrow &-4x & = &-24\\\Leftrightarrow & \color{red}{-4}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-24}{-4} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{-2}& = &12 \\\Leftrightarrow & -2x \color{red}{-2}\color{blue}{+2} & = &12\color{blue}{+2} \\\Leftrightarrow &-2x & = &14\\\Leftrightarrow & \color{red}{-2}x & = &14\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{14}{-2} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{-13}& = &-6 \\\Leftrightarrow & 8x \color{red}{-13}\color{blue}{+13} & = &-6\color{blue}{+13} \\\Leftrightarrow &8x & = &7\\\Leftrightarrow & \color{red}{8}x & = &7\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{7}{8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{+2}& = &-9 \\\Leftrightarrow & 5x \color{red}{+2}\color{blue}{-2} & = &-9\color{blue}{-2} \\\Leftrightarrow &5x & = &-11\\\Leftrightarrow & \color{red}{5}x & = &-11\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-11}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{5} } & & \\ & V = \left\{ \frac{-11}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{-8}& = &-14 \\\Leftrightarrow & -3x \color{red}{-8}\color{blue}{+8} & = &-14\color{blue}{+8} \\\Leftrightarrow &-3x & = &-6\\\Leftrightarrow & \color{red}{-3}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-6}{-3} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)