Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{+8}& = &-15 \\\Leftrightarrow & 12x \color{red}{+8}\color{blue}{-8} & = &-15\color{blue}{-8} \\\Leftrightarrow &12x & = &-23\\\Leftrightarrow & \color{red}{12}x & = &-23\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-23}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{12} } & & \\ & V = \left\{ \frac{-23}{12} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{-2}& = &-6 \\\Leftrightarrow & 8x \color{red}{-2}\color{blue}{+2} & = &-6\color{blue}{+2} \\\Leftrightarrow &8x & = &-4\\\Leftrightarrow & \color{red}{8}x & = &-4\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-4}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{-4}& = &2 \\\Leftrightarrow & 13x \color{red}{-4}\color{blue}{+4} & = &2\color{blue}{+4} \\\Leftrightarrow &13x & = &6\\\Leftrightarrow & \color{red}{13}x & = &6\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{6}{13} \\\Leftrightarrow & \color{green}{ x = \frac{6}{13} } & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{-13}& = &5 \\\Leftrightarrow & -9x \color{red}{-13}\color{blue}{+13} & = &5\color{blue}{+13} \\\Leftrightarrow &-9x & = &18\\\Leftrightarrow & \color{red}{-9}x & = &18\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{18}{-9} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{+14}& = &4 \\\Leftrightarrow & 14x \color{red}{+14}\color{blue}{-14} & = &4\color{blue}{-14} \\\Leftrightarrow &14x & = &-10\\\Leftrightarrow & \color{red}{14}x & = &-10\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-10}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{+1}& = &-2 \\\Leftrightarrow & -9x \color{red}{+1}\color{blue}{-1} & = &-2\color{blue}{-1} \\\Leftrightarrow &-9x & = &-3\\\Leftrightarrow & \color{red}{-9}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{+10}& = &-13 \\\Leftrightarrow & x \color{red}{+10}\color{blue}{-10} & = &-13\color{blue}{-10} \\\Leftrightarrow &x & = &-23\\\Leftrightarrow & \color{red}{}x & = &-23\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -23 \\\Leftrightarrow & \color{green}{ x = -23 } & & \\ & V = \left\{ -23 \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{+13}& = &11 \\\Leftrightarrow & 6x \color{red}{+13}\color{blue}{-13} & = &11\color{blue}{-13} \\\Leftrightarrow &6x & = &-2\\\Leftrightarrow & \color{red}{6}x & = &-2\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-2}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{+9}& = &-5 \\\Leftrightarrow & 6x \color{red}{+9}\color{blue}{-9} & = &-5\color{blue}{-9} \\\Leftrightarrow &6x & = &-14\\\Leftrightarrow & \color{red}{6}x & = &-14\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-14}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 15x \color{red}{+4}& = &13 \\\Leftrightarrow & 15x \color{red}{+4}\color{blue}{-4} & = &13\color{blue}{-4} \\\Leftrightarrow &15x & = &9\\\Leftrightarrow & \color{red}{15}x & = &9\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{9}{15} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{-5}& = &3 \\\Leftrightarrow & 4x \color{red}{-5}\color{blue}{+5} & = &3\color{blue}{+5} \\\Leftrightarrow &4x & = &8\\\Leftrightarrow & \color{red}{4}x & = &8\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{8}{4} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{-7}& = &-13 \\\Leftrightarrow & -8x \color{red}{-7}\color{blue}{+7} & = &-13\color{blue}{+7} \\\Leftrightarrow &-8x & = &-6\\\Leftrightarrow & \color{red}{-8}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-6}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)