Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{+11}& = &11 \\\Leftrightarrow & 8x \color{red}{+11}\color{blue}{-11} & = &11\color{blue}{-11} \\\Leftrightarrow &8x & = &0\\\Leftrightarrow & \color{red}{8}x & = &0\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{0}{8} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{+3}& = &9 \\\Leftrightarrow & 15x \color{red}{+3}\color{blue}{-3} & = &9\color{blue}{-3} \\\Leftrightarrow &15x & = &6\\\Leftrightarrow & \color{red}{15}x & = &6\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{6}{15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{+8}& = &-11 \\\Leftrightarrow & x \color{red}{+8}\color{blue}{-8} & = &-11\color{blue}{-8} \\\Leftrightarrow &x & = &-19\\\Leftrightarrow & \color{red}{}x & = &-19\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -19 \\\Leftrightarrow & \color{green}{ x = -19 } & & \\ & V = \left\{ -19 \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{+5}& = &6 \\\Leftrightarrow & 6x \color{red}{+5}\color{blue}{-5} & = &6\color{blue}{-5} \\\Leftrightarrow &6x & = &1\\\Leftrightarrow & \color{red}{6}x & = &1\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{1}{6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{-12}& = &-14 \\\Leftrightarrow & -8x \color{red}{-12}\color{blue}{+12} & = &-14\color{blue}{+12} \\\Leftrightarrow &-8x & = &-2\\\Leftrightarrow & \color{red}{-8}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-2}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{+11}& = &-5 \\\Leftrightarrow & 15x \color{red}{+11}\color{blue}{-11} & = &-5\color{blue}{-11} \\\Leftrightarrow &15x & = &-16\\\Leftrightarrow & \color{red}{15}x & = &-16\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-16}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{15} } & & \\ & V = \left\{ \frac{-16}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{+8}& = &-13 \\\Leftrightarrow & 11x \color{red}{+8}\color{blue}{-8} & = &-13\color{blue}{-8} \\\Leftrightarrow &11x & = &-21\\\Leftrightarrow & \color{red}{11}x & = &-21\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-21}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{11} } & & \\ & V = \left\{ \frac{-21}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{+2}& = &12 \\\Leftrightarrow & 13x \color{red}{+2}\color{blue}{-2} & = &12\color{blue}{-2} \\\Leftrightarrow &13x & = &10\\\Leftrightarrow & \color{red}{13}x & = &10\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{10}{13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -9x \color{red}{+2}& = &7 \\\Leftrightarrow & -9x \color{red}{+2}\color{blue}{-2} & = &7\color{blue}{-2} \\\Leftrightarrow &-9x & = &5\\\Leftrightarrow & \color{red}{-9}x & = &5\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{5}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{9} } & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{-13}& = &7 \\\Leftrightarrow & 6x \color{red}{-13}\color{blue}{+13} & = &7\color{blue}{+13} \\\Leftrightarrow &6x & = &20\\\Leftrightarrow & \color{red}{6}x & = &20\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{20}{6} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{+3}& = &-7 \\\Leftrightarrow & 10x \color{red}{+3}\color{blue}{-3} & = &-7\color{blue}{-3} \\\Leftrightarrow &10x & = &-10\\\Leftrightarrow & \color{red}{10}x & = &-10\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-10}{10} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{-14}& = &1 \\\Leftrightarrow & 12x \color{red}{-14}\color{blue}{+14} & = &1\color{blue}{+14} \\\Leftrightarrow &12x & = &15\\\Leftrightarrow & \color{red}{12}x & = &15\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{15}{12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)