Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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