Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{-7}& = &-7 \\\Leftrightarrow & 12x \color{red}{-7}\color{blue}{+7} & = &-7\color{blue}{+7} \\\Leftrightarrow &12x & = &0\\\Leftrightarrow & \color{red}{12}x & = &0\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{0}{12} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{+5}& = &8 \\\Leftrightarrow & -10x \color{red}{+5}\color{blue}{-5} & = &8\color{blue}{-5} \\\Leftrightarrow &-10x & = &3\\\Leftrightarrow & \color{red}{-10}x & = &3\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{3}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{10} } & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{-2}& = &-8 \\\Leftrightarrow & 13x \color{red}{-2}\color{blue}{+2} & = &-8\color{blue}{+2} \\\Leftrightarrow &13x & = &-6\\\Leftrightarrow & \color{red}{13}x & = &-6\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-6}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{-13}& = &11 \\\Leftrightarrow & -3x \color{red}{-13}\color{blue}{+13} & = &11\color{blue}{+13} \\\Leftrightarrow &-3x & = &24\\\Leftrightarrow & \color{red}{-3}x & = &24\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{24}{-3} \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{+6}& = &5 \\\Leftrightarrow & -7x \color{red}{+6}\color{blue}{-6} & = &5\color{blue}{-6} \\\Leftrightarrow &-7x & = &-1\\\Leftrightarrow & \color{red}{-7}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{+6}& = &15 \\\Leftrightarrow & -8x \color{red}{+6}\color{blue}{-6} & = &15\color{blue}{-6} \\\Leftrightarrow &-8x & = &9\\\Leftrightarrow & \color{red}{-8}x & = &9\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{9}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{8} } & & \\ & V = \left\{ \frac{-9}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{-4}& = &8 \\\Leftrightarrow & 2x \color{red}{-4}\color{blue}{+4} & = &8\color{blue}{+4} \\\Leftrightarrow &2x & = &12\\\Leftrightarrow & \color{red}{2}x & = &12\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{12}{2} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{-9}& = &13 \\\Leftrightarrow & 7x \color{red}{-9}\color{blue}{+9} & = &13\color{blue}{+9} \\\Leftrightarrow &7x & = &22\\\Leftrightarrow & \color{red}{7}x & = &22\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{22}{7} \\\Leftrightarrow & \color{green}{ x = \frac{22}{7} } & & \\ & V = \left\{ \frac{22}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{-11}& = &12 \\\Leftrightarrow & 8x \color{red}{-11}\color{blue}{+11} & = &12\color{blue}{+11} \\\Leftrightarrow &8x & = &23\\\Leftrightarrow & \color{red}{8}x & = &23\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{23}{8} \\\Leftrightarrow & \color{green}{ x = \frac{23}{8} } & & \\ & V = \left\{ \frac{23}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{-11}& = &5 \\\Leftrightarrow & 14x \color{red}{-11}\color{blue}{+11} & = &5\color{blue}{+11} \\\Leftrightarrow &14x & = &16\\\Leftrightarrow & \color{red}{14}x & = &16\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{16}{14} \\\Leftrightarrow & \color{green}{ x = \frac{8}{7} } & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{+6}& = &-9 \\\Leftrightarrow & 6x \color{red}{+6}\color{blue}{-6} & = &-9\color{blue}{-6} \\\Leftrightarrow &6x & = &-15\\\Leftrightarrow & \color{red}{6}x & = &-15\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-15}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{+10}& = &4 \\\Leftrightarrow & -13x \color{red}{+10}\color{blue}{-10} & = &4\color{blue}{-10} \\\Leftrightarrow &-13x & = &-6\\\Leftrightarrow & \color{red}{-13}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{6}{13} } & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)