Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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