Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & x \color{red}{+3}& = &-13 \\\Leftrightarrow & x \color{red}{+3}\color{blue}{-3} & = &-13\color{blue}{-3} \\\Leftrightarrow &x & = &-16\\\Leftrightarrow & \color{red}{}x & = &-16\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -16 \\\Leftrightarrow & \color{green}{ x = -16 } & & \\ & V = \left\{ -16 \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{+7}& = &-14 \\\Leftrightarrow & 5x \color{red}{+7}\color{blue}{-7} & = &-14\color{blue}{-7} \\\Leftrightarrow &5x & = &-21\\\Leftrightarrow & \color{red}{5}x & = &-21\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-21}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{5} } & & \\ & V = \left\{ \frac{-21}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{+11}& = &-11 \\\Leftrightarrow & -5x \color{red}{+11}\color{blue}{-11} & = &-11\color{blue}{-11} \\\Leftrightarrow &-5x & = &-22\\\Leftrightarrow & \color{red}{-5}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-22}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{22}{5} } & & \\ & V = \left\{ \frac{22}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{+6}& = &8 \\\Leftrightarrow & 13x \color{red}{+6}\color{blue}{-6} & = &8\color{blue}{-6} \\\Leftrightarrow &13x & = &2\\\Leftrightarrow & \color{red}{13}x & = &2\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{2}{13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{+2}& = &7 \\\Leftrightarrow & 11x \color{red}{+2}\color{blue}{-2} & = &7\color{blue}{-2} \\\Leftrightarrow &11x & = &5\\\Leftrightarrow & \color{red}{11}x & = &5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{+13}& = &-15 \\\Leftrightarrow & 12x \color{red}{+13}\color{blue}{-13} & = &-15\color{blue}{-13} \\\Leftrightarrow &12x & = &-28\\\Leftrightarrow & \color{red}{12}x & = &-28\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-28}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{+13}& = &8 \\\Leftrightarrow & -4x \color{red}{+13}\color{blue}{-13} & = &8\color{blue}{-13} \\\Leftrightarrow &-4x & = &-5\\\Leftrightarrow & \color{red}{-4}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-5}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{-9}& = &-2 \\\Leftrightarrow & 8x \color{red}{-9}\color{blue}{+9} & = &-2\color{blue}{+9} \\\Leftrightarrow &8x & = &7\\\Leftrightarrow & \color{red}{8}x & = &7\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{7}{8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{+6}& = &7 \\\Leftrightarrow & -10x \color{red}{+6}\color{blue}{-6} & = &7\color{blue}{-6} \\\Leftrightarrow &-10x & = &1\\\Leftrightarrow & \color{red}{-10}x & = &1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{+10}& = &-5 \\\Leftrightarrow & 10x \color{red}{+10}\color{blue}{-10} & = &-5\color{blue}{-10} \\\Leftrightarrow &10x & = &-15\\\Leftrightarrow & \color{red}{10}x & = &-15\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-15}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{+9}& = &-6 \\\Leftrightarrow & 7x \color{red}{+9}\color{blue}{-9} & = &-6\color{blue}{-9} \\\Leftrightarrow &7x & = &-15\\\Leftrightarrow & \color{red}{7}x & = &-15\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-15}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{7} } & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{-3}& = &6 \\\Leftrightarrow & 15x \color{red}{-3}\color{blue}{+3} & = &6\color{blue}{+3} \\\Leftrightarrow &15x & = &9\\\Leftrightarrow & \color{red}{15}x & = &9\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{9}{15} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)