Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{-10}& = &-10 \\\Leftrightarrow & 13x \color{red}{-10}\color{blue}{+10} & = &-10\color{blue}{+10} \\\Leftrightarrow &13x & = &0\\\Leftrightarrow & \color{red}{13}x & = &0\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{0}{13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{+12}& = &7 \\\Leftrightarrow & -10x \color{red}{+12}\color{blue}{-12} & = &7\color{blue}{-12} \\\Leftrightarrow &-10x & = &-5\\\Leftrightarrow & \color{red}{-10}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-5}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{-13}& = &6 \\\Leftrightarrow & -9x \color{red}{-13}\color{blue}{+13} & = &6\color{blue}{+13} \\\Leftrightarrow &-9x & = &19\\\Leftrightarrow & \color{red}{-9}x & = &19\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{19}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{9} } & & \\ & V = \left\{ \frac{-19}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{+10}& = &-12 \\\Leftrightarrow & 14x \color{red}{+10}\color{blue}{-10} & = &-12\color{blue}{-10} \\\Leftrightarrow &14x & = &-22\\\Leftrightarrow & \color{red}{14}x & = &-22\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-22}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{7} } & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{+3}& = &-9 \\\Leftrightarrow & -13x \color{red}{+3}\color{blue}{-3} & = &-9\color{blue}{-3} \\\Leftrightarrow &-13x & = &-12\\\Leftrightarrow & \color{red}{-13}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{12}{13} } & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{-15}& = &10 \\\Leftrightarrow & 7x \color{red}{-15}\color{blue}{+15} & = &10\color{blue}{+15} \\\Leftrightarrow &7x & = &25\\\Leftrightarrow & \color{red}{7}x & = &25\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{25}{7} \\\Leftrightarrow & \color{green}{ x = \frac{25}{7} } & & \\ & V = \left\{ \frac{25}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{+3}& = &8 \\\Leftrightarrow & -6x \color{red}{+3}\color{blue}{-3} & = &8\color{blue}{-3} \\\Leftrightarrow &-6x & = &5\\\Leftrightarrow & \color{red}{-6}x & = &5\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{5}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{-15}& = &-2 \\\Leftrightarrow & 8x \color{red}{-15}\color{blue}{+15} & = &-2\color{blue}{+15} \\\Leftrightarrow &8x & = &13\\\Leftrightarrow & \color{red}{8}x & = &13\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{13}{8} \\\Leftrightarrow & \color{green}{ x = \frac{13}{8} } & & \\ & V = \left\{ \frac{13}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{-11}& = &-11 \\\Leftrightarrow & -2x \color{red}{-11}\color{blue}{+11} & = &-11\color{blue}{+11} \\\Leftrightarrow &-2x & = &0\\\Leftrightarrow & \color{red}{-2}x & = &0\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{0}{-2} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{+10}& = &1 \\\Leftrightarrow & -10x \color{red}{+10}\color{blue}{-10} & = &1\color{blue}{-10} \\\Leftrightarrow &-10x & = &-9\\\Leftrightarrow & \color{red}{-10}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-9}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{9}{10} } & & \\ & V = \left\{ \frac{9}{10} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{-15}& = &-4 \\\Leftrightarrow & 10x \color{red}{-15}\color{blue}{+15} & = &-4\color{blue}{+15} \\\Leftrightarrow &10x & = &11\\\Leftrightarrow & \color{red}{10}x & = &11\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{11}{10} \\\Leftrightarrow & \color{green}{ x = \frac{11}{10} } & & \\ & V = \left\{ \frac{11}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{-2}& = &1 \\\Leftrightarrow & 4x \color{red}{-2}\color{blue}{+2} & = &1\color{blue}{+2} \\\Leftrightarrow &4x & = &3\\\Leftrightarrow & \color{red}{4}x & = &3\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{3}{4} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)