Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{+2}& = &8 \\\Leftrightarrow & 9x \color{red}{+2}\color{blue}{-2} & = &8\color{blue}{-2} \\\Leftrightarrow &9x & = &6\\\Leftrightarrow & \color{red}{9}x & = &6\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{6}{9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{+12}& = &13 \\\Leftrightarrow & -13x \color{red}{+12}\color{blue}{-12} & = &13\color{blue}{-12} \\\Leftrightarrow &-13x & = &1\\\Leftrightarrow & \color{red}{-13}x & = &1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{-8}& = &-13 \\\Leftrightarrow & -15x \color{red}{-8}\color{blue}{+8} & = &-13\color{blue}{+8} \\\Leftrightarrow &-15x & = &-5\\\Leftrightarrow & \color{red}{-15}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{-7}& = &9 \\\Leftrightarrow & -12x \color{red}{-7}\color{blue}{+7} & = &9\color{blue}{+7} \\\Leftrightarrow &-12x & = &16\\\Leftrightarrow & \color{red}{-12}x & = &16\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{16}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
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. \(\begin{align} & 8x \color{red}{-12}& = &15 \\\Leftrightarrow & 8x \color{red}{-12}\color{blue}{+12} & = &15\color{blue}{+12} \\\Leftrightarrow &8x & = &27\\\Leftrightarrow & \color{red}{8}x & = &27\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{27}{8} \\\Leftrightarrow & \color{green}{ x = \frac{27}{8} } & & \\ & V = \left\{ \frac{27}{8} \right\} & \\\end{align}\)
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. \(\begin{align} & 6x \color{red}{-2}& = &-2 \\\Leftrightarrow & 6x \color{red}{-2}\color{blue}{+2} & = &-2\color{blue}{+2} \\\Leftrightarrow &6x & = &0\\\Leftrightarrow & \color{red}{6}x & = &0\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{0}{6} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{+3}& = &4 \\\Leftrightarrow & -12x \color{red}{+3}\color{blue}{-3} & = &4\color{blue}{-3} \\\Leftrightarrow &-12x & = &1\\\Leftrightarrow & \color{red}{-12}x & = &1\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{1}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{12} } & & \\ & V = \left\{ \frac{-1}{12} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{+14}& = &-12 \\\Leftrightarrow & -6x \color{red}{+14}\color{blue}{-14} & = &-12\color{blue}{-14} \\\Leftrightarrow &-6x & = &-26\\\Leftrightarrow & \color{red}{-6}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-26}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{13}{3} } & & \\ & V = \left\{ \frac{13}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{+7}& = &11 \\\Leftrightarrow & 12x \color{red}{+7}\color{blue}{-7} & = &11\color{blue}{-7} \\\Leftrightarrow &12x & = &4\\\Leftrightarrow & \color{red}{12}x & = &4\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{4}{12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{+13}& = &1 \\\Leftrightarrow & -5x \color{red}{+13}\color{blue}{-13} & = &1\color{blue}{-13} \\\Leftrightarrow &-5x & = &-12\\\Leftrightarrow & \color{red}{-5}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-12}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)