Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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