Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{-6}& = &11 \\\Leftrightarrow & -6x \color{red}{-6}\color{blue}{+6} & = &11\color{blue}{+6} \\\Leftrightarrow &-6x & = &17\\\Leftrightarrow & \color{red}{-6}x & = &17\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{17}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{6} } & & \\ & V = \left\{ \frac{-17}{6} \right\} & \\\end{align}\)
2. \(\begin{align} & 13x \color{red}{-7}& = &3 \\\Leftrightarrow & 13x \color{red}{-7}\color{blue}{+7} & = &3\color{blue}{+7} \\\Leftrightarrow &13x & = &10\\\Leftrightarrow & \color{red}{13}x & = &10\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{10}{13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{+7}& = &10 \\\Leftrightarrow & -10x \color{red}{+7}\color{blue}{-7} & = &10\color{blue}{-7} \\\Leftrightarrow &-10x & = &3\\\Leftrightarrow & \color{red}{-10}x & = &3\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{3}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{10} } & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{-15}& = &-14 \\\Leftrightarrow & 14x \color{red}{-15}\color{blue}{+15} & = &-14\color{blue}{+15} \\\Leftrightarrow &14x & = &1\\\Leftrightarrow & \color{red}{14}x & = &1\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{1}{14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{14} } & & \\ & V = \left\{ \frac{1}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{-1}& = &-11 \\\Leftrightarrow & -3x \color{red}{-1}\color{blue}{+1} & = &-11\color{blue}{+1} \\\Leftrightarrow &-3x & = &-10\\\Leftrightarrow & \color{red}{-3}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-10}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{-3}& = &-8 \\\Leftrightarrow & 7x \color{red}{-3}\color{blue}{+3} & = &-8\color{blue}{+3} \\\Leftrightarrow &7x & = &-5\\\Leftrightarrow & \color{red}{7}x & = &-5\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-5}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{-3}& = &-13 \\\Leftrightarrow & -11x \color{red}{-3}\color{blue}{+3} & = &-13\color{blue}{+3} \\\Leftrightarrow &-11x & = &-10\\\Leftrightarrow & \color{red}{-11}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-10}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{10}{11} } & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{-15}& = &10 \\\Leftrightarrow & -5x \color{red}{-15}\color{blue}{+15} & = &10\color{blue}{+15} \\\Leftrightarrow &-5x & = &25\\\Leftrightarrow & \color{red}{-5}x & = &25\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{25}{-5} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{+5}& = &-4 \\\Leftrightarrow & 8x \color{red}{+5}\color{blue}{-5} & = &-4\color{blue}{-5} \\\Leftrightarrow &8x & = &-9\\\Leftrightarrow & \color{red}{8}x & = &-9\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-9}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{8} } & & \\ & V = \left\{ \frac{-9}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{-10}& = &-15 \\\Leftrightarrow & 10x \color{red}{-10}\color{blue}{+10} & = &-15\color{blue}{+10} \\\Leftrightarrow &10x & = &-5\\\Leftrightarrow & \color{red}{10}x & = &-5\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-5}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{-2}& = &3 \\\Leftrightarrow & 11x \color{red}{-2}\color{blue}{+2} & = &3\color{blue}{+2} \\\Leftrightarrow &11x & = &5\\\Leftrightarrow & \color{red}{11}x & = &5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{-14}& = &-13 \\\Leftrightarrow & 8x \color{red}{-14}\color{blue}{+14} & = &-13\color{blue}{+14} \\\Leftrightarrow &8x & = &1\\\Leftrightarrow & \color{red}{8}x & = &1\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{1}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)