Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{+7}& = &6 \\\Leftrightarrow & -8x \color{red}{+7}\color{blue}{-7} & = &6\color{blue}{-7} \\\Leftrightarrow &-8x & = &-1\\\Leftrightarrow & \color{red}{-8}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{-10}& = &14 \\\Leftrightarrow & -12x \color{red}{-10}\color{blue}{+10} & = &14\color{blue}{+10} \\\Leftrightarrow &-12x & = &24\\\Leftrightarrow & \color{red}{-12}x & = &24\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{24}{-12} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{+3}& = &-10 \\\Leftrightarrow & -x \color{red}{+3}\color{blue}{-3} & = &-10\color{blue}{-3} \\\Leftrightarrow &-x & = &-13\\\Leftrightarrow & \color{red}{-}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-13}{-1} \\\Leftrightarrow & \color{green}{ x = 13 } & & \\ & V = \left\{ 13 \right\} & \\\end{align}\)
4. \(\begin{align} & x \color{red}{+10}& = &-11 \\\Leftrightarrow & x \color{red}{+10}\color{blue}{-10} & = &-11\color{blue}{-10} \\\Leftrightarrow &x & = &-21\\\Leftrightarrow & \color{red}{}x & = &-21\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -21 \\\Leftrightarrow & \color{green}{ x = -21 } & & \\ & V = \left\{ -21 \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{-11}& = &2 \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11} & = &2\color{blue}{+11} \\\Leftrightarrow &-5x & = &13\\\Leftrightarrow & \color{red}{-5}x & = &13\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{13}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{5} } & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{+11}& = &8 \\\Leftrightarrow & -13x \color{red}{+11}\color{blue}{-11} & = &8\color{blue}{-11} \\\Leftrightarrow &-13x & = &-3\\\Leftrightarrow & \color{red}{-13}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{3}{13} } & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{-7}& = &11 \\\Leftrightarrow & -2x \color{red}{-7}\color{blue}{+7} & = &11\color{blue}{+7} \\\Leftrightarrow &-2x & = &18\\\Leftrightarrow & \color{red}{-2}x & = &18\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{18}{-2} \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{+3}& = &4 \\\Leftrightarrow & 8x \color{red}{+3}\color{blue}{-3} & = &4\color{blue}{-3} \\\Leftrightarrow &8x & = &1\\\Leftrightarrow & \color{red}{8}x & = &1\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{1}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{-15}& = &3 \\\Leftrightarrow & 7x \color{red}{-15}\color{blue}{+15} & = &3\color{blue}{+15} \\\Leftrightarrow &7x & = &18\\\Leftrightarrow & \color{red}{7}x & = &18\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{18}{7} \\\Leftrightarrow & \color{green}{ x = \frac{18}{7} } & & \\ & V = \left\{ \frac{18}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{-14}& = &13 \\\Leftrightarrow & 10x \color{red}{-14}\color{blue}{+14} & = &13\color{blue}{+14} \\\Leftrightarrow &10x & = &27\\\Leftrightarrow & \color{red}{10}x & = &27\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{27}{10} \\\Leftrightarrow & \color{green}{ x = \frac{27}{10} } & & \\ & V = \left\{ \frac{27}{10} \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{-4}& = &2 \\\Leftrightarrow & -8x \color{red}{-4}\color{blue}{+4} & = &2\color{blue}{+4} \\\Leftrightarrow &-8x & = &6\\\Leftrightarrow & \color{red}{-8}x & = &6\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{6}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{-4}& = &-7 \\\Leftrightarrow & 13x \color{red}{-4}\color{blue}{+4} & = &-7\color{blue}{+4} \\\Leftrightarrow &13x & = &-3\\\Leftrightarrow & \color{red}{13}x & = &-3\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-3}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)