Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{+12}& = &-8 \\\Leftrightarrow & 3x \color{red}{+12}\color{blue}{-12} & = &-8\color{blue}{-12} \\\Leftrightarrow &3x & = &-20\\\Leftrightarrow & \color{red}{3}x & = &-20\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-20}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{3} } & & \\ & V = \left\{ \frac{-20}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{+6}& = &-7 \\\Leftrightarrow & 11x \color{red}{+6}\color{blue}{-6} & = &-7\color{blue}{-6} \\\Leftrightarrow &11x & = &-13\\\Leftrightarrow & \color{red}{11}x & = &-13\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-13}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{11} } & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{+1}& = &-4 \\\Leftrightarrow & 15x \color{red}{+1}\color{blue}{-1} & = &-4\color{blue}{-1} \\\Leftrightarrow &15x & = &-5\\\Leftrightarrow & \color{red}{15}x & = &-5\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-5}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{-10}& = &4 \\\Leftrightarrow & 15x \color{red}{-10}\color{blue}{+10} & = &4\color{blue}{+10} \\\Leftrightarrow &15x & = &14\\\Leftrightarrow & \color{red}{15}x & = &14\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{14}{15} \\\Leftrightarrow & \color{green}{ x = \frac{14}{15} } & & \\ & V = \left\{ \frac{14}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{+13}& = &11 \\\Leftrightarrow & -9x \color{red}{+13}\color{blue}{-13} & = &11\color{blue}{-13} \\\Leftrightarrow &-9x & = &-2\\\Leftrightarrow & \color{red}{-9}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{9} } & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{-12}& = &-1 \\\Leftrightarrow & x \color{red}{-12}\color{blue}{+12} & = &-1\color{blue}{+12} \\\Leftrightarrow &x & = &11\\\Leftrightarrow & \color{red}{}x & = &11\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 11 \\\Leftrightarrow & \color{green}{ x = 11 } & & \\ & V = \left\{ 11 \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{-12}& = &9 \\\Leftrightarrow & -10x \color{red}{-12}\color{blue}{+12} & = &9\color{blue}{+12} \\\Leftrightarrow &-10x & = &21\\\Leftrightarrow & \color{red}{-10}x & = &21\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{21}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{10} } & & \\ & V = \left\{ \frac{-21}{10} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{+3}& = &6 \\\Leftrightarrow & -14x \color{red}{+3}\color{blue}{-3} & = &6\color{blue}{-3} \\\Leftrightarrow &-14x & = &3\\\Leftrightarrow & \color{red}{-14}x & = &3\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{3}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{14} } & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{+14}& = &-4 \\\Leftrightarrow & -8x \color{red}{+14}\color{blue}{-14} & = &-4\color{blue}{-14} \\\Leftrightarrow &-8x & = &-18\\\Leftrightarrow & \color{red}{-8}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-18}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{-5}& = &4 \\\Leftrightarrow & -x \color{red}{-5}\color{blue}{+5} & = &4\color{blue}{+5} \\\Leftrightarrow &-x & = &9\\\Leftrightarrow & \color{red}{-}x & = &9\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{9}{-1} \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{+6}& = &4 \\\Leftrightarrow & -6x \color{red}{+6}\color{blue}{-6} & = &4\color{blue}{-6} \\\Leftrightarrow &-6x & = &-2\\\Leftrightarrow & \color{red}{-6}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{+3}& = &11 \\\Leftrightarrow & 5x \color{red}{+3}\color{blue}{-3} & = &11\color{blue}{-3} \\\Leftrightarrow &5x & = &8\\\Leftrightarrow & \color{red}{5}x & = &8\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{8}{5} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)