Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{-4}& = &-13 \\\Leftrightarrow & -2x \color{red}{-4}\color{blue}{+4} & = &-13\color{blue}{+4} \\\Leftrightarrow &-2x & = &-9\\\Leftrightarrow & \color{red}{-2}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-9}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{9}{2} } & & \\ & V = \left\{ \frac{9}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{-12}& = &13 \\\Leftrightarrow & -2x \color{red}{-12}\color{blue}{+12} & = &13\color{blue}{+12} \\\Leftrightarrow &-2x & = &25\\\Leftrightarrow & \color{red}{-2}x & = &25\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{25}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{2} } & & \\ & V = \left\{ \frac{-25}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{-11}& = &12 \\\Leftrightarrow & 9x \color{red}{-11}\color{blue}{+11} & = &12\color{blue}{+11} \\\Leftrightarrow &9x & = &23\\\Leftrightarrow & \color{red}{9}x & = &23\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{23}{9} \\\Leftrightarrow & \color{green}{ x = \frac{23}{9} } & & \\ & V = \left\{ \frac{23}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{+9}& = &-11 \\\Leftrightarrow & -5x \color{red}{+9}\color{blue}{-9} & = &-11\color{blue}{-9} \\\Leftrightarrow &-5x & = &-20\\\Leftrightarrow & \color{red}{-5}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-20}{-5} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{-7}& = &-13 \\\Leftrightarrow & -11x \color{red}{-7}\color{blue}{+7} & = &-13\color{blue}{+7} \\\Leftrightarrow &-11x & = &-6\\\Leftrightarrow & \color{red}{-11}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-6}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{6}{11} } & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{+5}& = &3 \\\Leftrightarrow & 5x \color{red}{+5}\color{blue}{-5} & = &3\color{blue}{-5} \\\Leftrightarrow &5x & = &-2\\\Leftrightarrow & \color{red}{5}x & = &-2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{-5}& = &8 \\\Leftrightarrow & -6x \color{red}{-5}\color{blue}{+5} & = &8\color{blue}{+5} \\\Leftrightarrow &-6x & = &13\\\Leftrightarrow & \color{red}{-6}x & = &13\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{13}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{6} } & & \\ & V = \left\{ \frac{-13}{6} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{-4}& = &-6 \\\Leftrightarrow & 8x \color{red}{-4}\color{blue}{+4} & = &-6\color{blue}{+4} \\\Leftrightarrow &8x & = &-2\\\Leftrightarrow & \color{red}{8}x & = &-2\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-2}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{-12}& = &-11 \\\Leftrightarrow & 10x \color{red}{-12}\color{blue}{+12} & = &-11\color{blue}{+12} \\\Leftrightarrow &10x & = &1\\\Leftrightarrow & \color{red}{10}x & = &1\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{1}{10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{10} } & & \\ & V = \left\{ \frac{1}{10} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{-3}& = &-5 \\\Leftrightarrow & 6x \color{red}{-3}\color{blue}{+3} & = &-5\color{blue}{+3} \\\Leftrightarrow &6x & = &-2\\\Leftrightarrow & \color{red}{6}x & = &-2\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-2}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{-7}& = &3 \\\Leftrightarrow & -6x \color{red}{-7}\color{blue}{+7} & = &3\color{blue}{+7} \\\Leftrightarrow &-6x & = &10\\\Leftrightarrow & \color{red}{-6}x & = &10\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{10}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{-10}& = &-13 \\\Leftrightarrow & -x \color{red}{-10}\color{blue}{+10} & = &-13\color{blue}{+10} \\\Leftrightarrow &-x & = &-3\\\Leftrightarrow & \color{red}{-}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-3}{-1} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)