Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{-12}& = &-3 \\\Leftrightarrow & 9x \color{red}{-12}\color{blue}{+12} & = &-3\color{blue}{+12} \\\Leftrightarrow &9x & = &9\\\Leftrightarrow & \color{red}{9}x & = &9\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{9}{9} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{+15}& = &-14 \\\Leftrightarrow & -x \color{red}{+15}\color{blue}{-15} & = &-14\color{blue}{-15} \\\Leftrightarrow &-x & = &-29\\\Leftrightarrow & \color{red}{-}x & = &-29\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-29}{-1} \\\Leftrightarrow & \color{green}{ x = 29 } & & \\ & V = \left\{ 29 \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{-5}& = &7 \\\Leftrightarrow & -9x \color{red}{-5}\color{blue}{+5} & = &7\color{blue}{+5} \\\Leftrightarrow &-9x & = &12\\\Leftrightarrow & \color{red}{-9}x & = &12\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{12}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{+6}& = &-6 \\\Leftrightarrow & -15x \color{red}{+6}\color{blue}{-6} & = &-6\color{blue}{-6} \\\Leftrightarrow &-15x & = &-12\\\Leftrightarrow & \color{red}{-15}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{-14}& = &7 \\\Leftrightarrow & 9x \color{red}{-14}\color{blue}{+14} & = &7\color{blue}{+14} \\\Leftrightarrow &9x & = &21\\\Leftrightarrow & \color{red}{9}x & = &21\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{21}{9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{+11}& = &10 \\\Leftrightarrow & -11x \color{red}{+11}\color{blue}{-11} & = &10\color{blue}{-11} \\\Leftrightarrow &-11x & = &-1\\\Leftrightarrow & \color{red}{-11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{+12}& = &10 \\\Leftrightarrow & 3x \color{red}{+12}\color{blue}{-12} & = &10\color{blue}{-12} \\\Leftrightarrow &3x & = &-2\\\Leftrightarrow & \color{red}{3}x & = &-2\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-2}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{+7}& = &15 \\\Leftrightarrow & -11x \color{red}{+7}\color{blue}{-7} & = &15\color{blue}{-7} \\\Leftrightarrow &-11x & = &8\\\Leftrightarrow & \color{red}{-11}x & = &8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{11} } & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{+10}& = &8 \\\Leftrightarrow & -6x \color{red}{+10}\color{blue}{-10} & = &8\color{blue}{-10} \\\Leftrightarrow &-6x & = &-2\\\Leftrightarrow & \color{red}{-6}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{+9}& = &10 \\\Leftrightarrow & -x \color{red}{+9}\color{blue}{-9} & = &10\color{blue}{-9} \\\Leftrightarrow &-x & = &1\\\Leftrightarrow & \color{red}{-}x & = &1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{1}{-1} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{-9}& = &-5 \\\Leftrightarrow & -15x \color{red}{-9}\color{blue}{+9} & = &-5\color{blue}{+9} \\\Leftrightarrow &-15x & = &4\\\Leftrightarrow & \color{red}{-15}x & = &4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{15} } & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{-15}& = &9 \\\Leftrightarrow & -12x \color{red}{-15}\color{blue}{+15} & = &9\color{blue}{+15} \\\Leftrightarrow &-12x & = &24\\\Leftrightarrow & \color{red}{-12}x & = &24\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{24}{-12} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)