Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{+8}& = &4 \\\Leftrightarrow & -11x \color{red}{+8}\color{blue}{-8} & = &4\color{blue}{-8} \\\Leftrightarrow &-11x & = &-4\\\Leftrightarrow & \color{red}{-11}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-4}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{4}{11} } & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 13x \color{red}{-2}& = &-13 \\\Leftrightarrow & 13x \color{red}{-2}\color{blue}{+2} & = &-13\color{blue}{+2} \\\Leftrightarrow &13x & = &-11\\\Leftrightarrow & \color{red}{13}x & = &-11\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-11}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{13} } & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{+13}& = &-14 \\\Leftrightarrow & -2x \color{red}{+13}\color{blue}{-13} & = &-14\color{blue}{-13} \\\Leftrightarrow &-2x & = &-27\\\Leftrightarrow & \color{red}{-2}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-27}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{27}{2} } & & \\ & V = \left\{ \frac{27}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{+3}& = &-14 \\\Leftrightarrow & -x \color{red}{+3}\color{blue}{-3} & = &-14\color{blue}{-3} \\\Leftrightarrow &-x & = &-17\\\Leftrightarrow & \color{red}{-}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-17}{-1} \\\Leftrightarrow & \color{green}{ x = 17 } & & \\ & V = \left\{ 17 \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{-14}& = &-11 \\\Leftrightarrow & -5x \color{red}{-14}\color{blue}{+14} & = &-11\color{blue}{+14} \\\Leftrightarrow &-5x & = &3\\\Leftrightarrow & \color{red}{-5}x & = &3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{-12}& = &-14 \\\Leftrightarrow & 8x \color{red}{-12}\color{blue}{+12} & = &-14\color{blue}{+12} \\\Leftrightarrow &8x & = &-2\\\Leftrightarrow & \color{red}{8}x & = &-2\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-2}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{+6}& = &12 \\\Leftrightarrow & -4x \color{red}{+6}\color{blue}{-6} & = &12\color{blue}{-6} \\\Leftrightarrow &-4x & = &6\\\Leftrightarrow & \color{red}{-4}x & = &6\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{6}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{-10}& = &-1 \\\Leftrightarrow & -12x \color{red}{-10}\color{blue}{+10} & = &-1\color{blue}{+10} \\\Leftrightarrow &-12x & = &9\\\Leftrightarrow & \color{red}{-12}x & = &9\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{9}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{+4}& = &-4 \\\Leftrightarrow & -2x \color{red}{+4}\color{blue}{-4} & = &-4\color{blue}{-4} \\\Leftrightarrow &-2x & = &-8\\\Leftrightarrow & \color{red}{-2}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-8}{-2} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{+14}& = &13 \\\Leftrightarrow & 9x \color{red}{+14}\color{blue}{-14} & = &13\color{blue}{-14} \\\Leftrightarrow &9x & = &-1\\\Leftrightarrow & \color{red}{9}x & = &-1\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-1}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{9} } & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{+7}& = &-11 \\\Leftrightarrow & 12x \color{red}{+7}\color{blue}{-7} & = &-11\color{blue}{-7} \\\Leftrightarrow &12x & = &-18\\\Leftrightarrow & \color{red}{12}x & = &-18\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-18}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{-11}& = &9 \\\Leftrightarrow & -2x \color{red}{-11}\color{blue}{+11} & = &9\color{blue}{+11} \\\Leftrightarrow &-2x & = &20\\\Leftrightarrow & \color{red}{-2}x & = &20\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{20}{-2} \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)