Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{-7}& = &-7 \\\Leftrightarrow & 8x \color{red}{-7}\color{blue}{+7} & = &-7\color{blue}{+7} \\\Leftrightarrow &8x & = &0\\\Leftrightarrow & \color{red}{8}x & = &0\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{0}{8} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{+6}& = &-14 \\\Leftrightarrow & -15x \color{red}{+6}\color{blue}{-6} & = &-14\color{blue}{-6} \\\Leftrightarrow &-15x & = &-20\\\Leftrightarrow & \color{red}{-15}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-20}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{+6}& = &-3 \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6} & = &-3\color{blue}{-6} \\\Leftrightarrow &15x & = &-9\\\Leftrightarrow & \color{red}{15}x & = &-9\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-9}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{+6}& = &9 \\\Leftrightarrow & 11x \color{red}{+6}\color{blue}{-6} & = &9\color{blue}{-6} \\\Leftrightarrow &11x & = &3\\\Leftrightarrow & \color{red}{11}x & = &3\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{3}{11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{-13}& = &10 \\\Leftrightarrow & -14x \color{red}{-13}\color{blue}{+13} & = &10\color{blue}{+13} \\\Leftrightarrow &-14x & = &23\\\Leftrightarrow & \color{red}{-14}x & = &23\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{23}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{14} } & & \\ & V = \left\{ \frac{-23}{14} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{+12}& = &-8 \\\Leftrightarrow & -5x \color{red}{+12}\color{blue}{-12} & = &-8\color{blue}{-12} \\\Leftrightarrow &-5x & = &-20\\\Leftrightarrow & \color{red}{-5}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-20}{-5} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{-4}& = &-11 \\\Leftrightarrow & -12x \color{red}{-4}\color{blue}{+4} & = &-11\color{blue}{+4} \\\Leftrightarrow &-12x & = &-7\\\Leftrightarrow & \color{red}{-12}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-7}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{12} } & & \\ & V = \left\{ \frac{7}{12} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{+13}& = &1 \\\Leftrightarrow & 11x \color{red}{+13}\color{blue}{-13} & = &1\color{blue}{-13} \\\Leftrightarrow &11x & = &-12\\\Leftrightarrow & \color{red}{11}x & = &-12\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-12}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{11} } & & \\ & V = \left\{ \frac{-12}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{-8}& = &11 \\\Leftrightarrow & -15x \color{red}{-8}\color{blue}{+8} & = &11\color{blue}{+8} \\\Leftrightarrow &-15x & = &19\\\Leftrightarrow & \color{red}{-15}x & = &19\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{19}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{15} } & & \\ & V = \left\{ \frac{-19}{15} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{+6}& = &1 \\\Leftrightarrow & 12x \color{red}{+6}\color{blue}{-6} & = &1\color{blue}{-6} \\\Leftrightarrow &12x & = &-5\\\Leftrightarrow & \color{red}{12}x & = &-5\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-5}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{12} } & & \\ & V = \left\{ \frac{-5}{12} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{-8}& = &-14 \\\Leftrightarrow & -3x \color{red}{-8}\color{blue}{+8} & = &-14\color{blue}{+8} \\\Leftrightarrow &-3x & = &-6\\\Leftrightarrow & \color{red}{-3}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-6}{-3} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{+12}& = &-3 \\\Leftrightarrow & -2x \color{red}{+12}\color{blue}{-12} & = &-3\color{blue}{-12} \\\Leftrightarrow &-2x & = &-15\\\Leftrightarrow & \color{red}{-2}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-15}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{15}{2} } & & \\ & V = \left\{ \frac{15}{2} \right\} & \\\end{align}\)