Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{-12}& = &-14 \\\Leftrightarrow & -11x \color{red}{-12}\color{blue}{+12} & = &-14\color{blue}{+12} \\\Leftrightarrow &-11x & = &-2\\\Leftrightarrow & \color{red}{-11}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{+3}& = &-8 \\\Leftrightarrow & 12x \color{red}{+3}\color{blue}{-3} & = &-8\color{blue}{-3} \\\Leftrightarrow &12x & = &-11\\\Leftrightarrow & \color{red}{12}x & = &-11\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-11}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{12} } & & \\ & V = \left\{ \frac{-11}{12} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{+1}& = &13 \\\Leftrightarrow & -9x \color{red}{+1}\color{blue}{-1} & = &13\color{blue}{-1} \\\Leftrightarrow &-9x & = &12\\\Leftrightarrow & \color{red}{-9}x & = &12\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{12}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{-14}& = &11 \\\Leftrightarrow & 15x \color{red}{-14}\color{blue}{+14} & = &11\color{blue}{+14} \\\Leftrightarrow &15x & = &25\\\Leftrightarrow & \color{red}{15}x & = &25\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{25}{15} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{-13}& = &10 \\\Leftrightarrow & -13x \color{red}{-13}\color{blue}{+13} & = &10\color{blue}{+13} \\\Leftrightarrow &-13x & = &23\\\Leftrightarrow & \color{red}{-13}x & = &23\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{23}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{13} } & & \\ & V = \left\{ \frac{-23}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{+11}& = &-14 \\\Leftrightarrow & 6x \color{red}{+11}\color{blue}{-11} & = &-14\color{blue}{-11} \\\Leftrightarrow &6x & = &-25\\\Leftrightarrow & \color{red}{6}x & = &-25\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-25}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{6} } & & \\ & V = \left\{ \frac{-25}{6} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{+10}& = &1 \\\Leftrightarrow & 15x \color{red}{+10}\color{blue}{-10} & = &1\color{blue}{-10} \\\Leftrightarrow &15x & = &-9\\\Leftrightarrow & \color{red}{15}x & = &-9\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-9}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{+5}& = &9 \\\Leftrightarrow & 10x \color{red}{+5}\color{blue}{-5} & = &9\color{blue}{-5} \\\Leftrightarrow &10x & = &4\\\Leftrightarrow & \color{red}{10}x & = &4\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{4}{10} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{-12}& = &-9 \\\Leftrightarrow & -6x \color{red}{-12}\color{blue}{+12} & = &-9\color{blue}{+12} \\\Leftrightarrow &-6x & = &3\\\Leftrightarrow & \color{red}{-6}x & = &3\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{3}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{-7}& = &-5 \\\Leftrightarrow & -10x \color{red}{-7}\color{blue}{+7} & = &-5\color{blue}{+7} \\\Leftrightarrow &-10x & = &2\\\Leftrightarrow & \color{red}{-10}x & = &2\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{2}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{-7}& = &2 \\\Leftrightarrow & -10x \color{red}{-7}\color{blue}{+7} & = &2\color{blue}{+7} \\\Leftrightarrow &-10x & = &9\\\Leftrightarrow & \color{red}{-10}x & = &9\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{9}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{10} } & & \\ & V = \left\{ \frac{-9}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{-10}& = &3 \\\Leftrightarrow & -10x \color{red}{-10}\color{blue}{+10} & = &3\color{blue}{+10} \\\Leftrightarrow &-10x & = &13\\\Leftrightarrow & \color{red}{-10}x & = &13\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{13}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{10} } & & \\ & V = \left\{ \frac{-13}{10} \right\} & \\\end{align}\)