Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{-12}& = &-15 \\\Leftrightarrow & 12x \color{red}{-12}\color{blue}{+12} & = &-15\color{blue}{+12} \\\Leftrightarrow &12x & = &-3\\\Leftrightarrow & \color{red}{12}x & = &-3\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-3}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{+4}& = &-7 \\\Leftrightarrow & -4x \color{red}{+4}\color{blue}{-4} & = &-7\color{blue}{-4} \\\Leftrightarrow &-4x & = &-11\\\Leftrightarrow & \color{red}{-4}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-11}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{11}{4} } & & \\ & V = \left\{ \frac{11}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{+12}& = &13 \\\Leftrightarrow & 10x \color{red}{+12}\color{blue}{-12} & = &13\color{blue}{-12} \\\Leftrightarrow &10x & = &1\\\Leftrightarrow & \color{red}{10}x & = &1\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{1}{10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{10} } & & \\ & V = \left\{ \frac{1}{10} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-1}& = &4 \\\Leftrightarrow & -15x \color{red}{-1}\color{blue}{+1} & = &4\color{blue}{+1} \\\Leftrightarrow &-15x & = &5\\\Leftrightarrow & \color{red}{-15}x & = &5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{+12}& = &-8 \\\Leftrightarrow & 2x \color{red}{+12}\color{blue}{-12} & = &-8\color{blue}{-12} \\\Leftrightarrow &2x & = &-20\\\Leftrightarrow & \color{red}{2}x & = &-20\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-20}{2} \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{-8}& = &12 \\\Leftrightarrow & 6x \color{red}{-8}\color{blue}{+8} & = &12\color{blue}{+8} \\\Leftrightarrow &6x & = &20\\\Leftrightarrow & \color{red}{6}x & = &20\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{20}{6} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{+7}& = &4 \\\Leftrightarrow & 15x \color{red}{+7}\color{blue}{-7} & = &4\color{blue}{-7} \\\Leftrightarrow &15x & = &-3\\\Leftrightarrow & \color{red}{15}x & = &-3\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-3}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{-10}& = &-9 \\\Leftrightarrow & 13x \color{red}{-10}\color{blue}{+10} & = &-9\color{blue}{+10} \\\Leftrightarrow &13x & = &1\\\Leftrightarrow & \color{red}{13}x & = &1\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{1}{13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{-5}& = &4 \\\Leftrightarrow & 8x \color{red}{-5}\color{blue}{+5} & = &4\color{blue}{+5} \\\Leftrightarrow &8x & = &9\\\Leftrightarrow & \color{red}{8}x & = &9\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{9}{8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{8} } & & \\ & V = \left\{ \frac{9}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{+4}& = &5 \\\Leftrightarrow & 11x \color{red}{+4}\color{blue}{-4} & = &5\color{blue}{-4} \\\Leftrightarrow &11x & = &1\\\Leftrightarrow & \color{red}{11}x & = &1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{-13}& = &-15 \\\Leftrightarrow & 11x \color{red}{-13}\color{blue}{+13} & = &-15\color{blue}{+13} \\\Leftrightarrow &11x & = &-2\\\Leftrightarrow & \color{red}{11}x & = &-2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{-4}& = &14 \\\Leftrightarrow & 11x \color{red}{-4}\color{blue}{+4} & = &14\color{blue}{+4} \\\Leftrightarrow &11x & = &18\\\Leftrightarrow & \color{red}{11}x & = &18\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{18}{11} \\\Leftrightarrow & \color{green}{ x = \frac{18}{11} } & & \\ & V = \left\{ \frac{18}{11} \right\} & \\\end{align}\)