Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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