Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -x \color{red}{-10}& = &10 \\\Leftrightarrow & -x \color{red}{-10}\color{blue}{+10} & = &10\color{blue}{+10} \\\Leftrightarrow &-x & = &20\\\Leftrightarrow & \color{red}{-}x & = &20\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{20}{-1} \\\Leftrightarrow & \color{green}{ x = -20 } & & \\ & V = \left\{ -20 \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{-12}& = &-12 \\\Leftrightarrow & 2x \color{red}{-12}\color{blue}{+12} & = &-12\color{blue}{+12} \\\Leftrightarrow &2x & = &0\\\Leftrightarrow & \color{red}{2}x & = &0\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{0}{2} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{-15}& = &7 \\\Leftrightarrow & 6x \color{red}{-15}\color{blue}{+15} & = &7\color{blue}{+15} \\\Leftrightarrow &6x & = &22\\\Leftrightarrow & \color{red}{6}x & = &22\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{22}{6} \\\Leftrightarrow & \color{green}{ x = \frac{11}{3} } & & \\ & V = \left\{ \frac{11}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{-11}& = &9 \\\Leftrightarrow & 4x \color{red}{-11}\color{blue}{+11} & = &9\color{blue}{+11} \\\Leftrightarrow &4x & = &20\\\Leftrightarrow & \color{red}{4}x & = &20\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{20}{4} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{+15}& = &10 \\\Leftrightarrow & -5x \color{red}{+15}\color{blue}{-15} & = &10\color{blue}{-15} \\\Leftrightarrow &-5x & = &-5\\\Leftrightarrow & \color{red}{-5}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-5}{-5} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{+10}& = &1 \\\Leftrightarrow & -2x \color{red}{+10}\color{blue}{-10} & = &1\color{blue}{-10} \\\Leftrightarrow &-2x & = &-9\\\Leftrightarrow & \color{red}{-2}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-9}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{9}{2} } & & \\ & V = \left\{ \frac{9}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{-12}& = &12 \\\Leftrightarrow & 12x \color{red}{-12}\color{blue}{+12} & = &12\color{blue}{+12} \\\Leftrightarrow &12x & = &24\\\Leftrightarrow & \color{red}{12}x & = &24\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{24}{12} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{+4}& = &13 \\\Leftrightarrow & 11x \color{red}{+4}\color{blue}{-4} & = &13\color{blue}{-4} \\\Leftrightarrow &11x & = &9\\\Leftrightarrow & \color{red}{11}x & = &9\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{9}{11} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{-6}& = &8 \\\Leftrightarrow & -10x \color{red}{-6}\color{blue}{+6} & = &8\color{blue}{+6} \\\Leftrightarrow &-10x & = &14\\\Leftrightarrow & \color{red}{-10}x & = &14\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{14}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{-2}& = &8 \\\Leftrightarrow & 14x \color{red}{-2}\color{blue}{+2} & = &8\color{blue}{+2} \\\Leftrightarrow &14x & = &10\\\Leftrightarrow & \color{red}{14}x & = &10\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{10}{14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{+6}& = &7 \\\Leftrightarrow & 12x \color{red}{+6}\color{blue}{-6} & = &7\color{blue}{-6} \\\Leftrightarrow &12x & = &1\\\Leftrightarrow & \color{red}{12}x & = &1\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{1}{12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{12} } & & \\ & V = \left\{ \frac{1}{12} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{-12}& = &13 \\\Leftrightarrow & x \color{red}{-12}\color{blue}{+12} & = &13\color{blue}{+12} \\\Leftrightarrow &x & = &25\\\Leftrightarrow & \color{red}{}x & = &25\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 25 \\\Leftrightarrow & \color{green}{ x = 25 } & & \\ & V = \left\{ 25 \right\} & \\\end{align}\)