Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{+13}& = &-12 \\\Leftrightarrow & 15x \color{red}{+13}\color{blue}{-13} & = &-12\color{blue}{-13} \\\Leftrightarrow &15x & = &-25\\\Leftrightarrow & \color{red}{15}x & = &-25\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-25}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{-15}& = &-11 \\\Leftrightarrow & -8x \color{red}{-15}\color{blue}{+15} & = &-11\color{blue}{+15} \\\Leftrightarrow &-8x & = &4\\\Leftrightarrow & \color{red}{-8}x & = &4\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{4}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{+1}& = &1 \\\Leftrightarrow & 10x \color{red}{+1}\color{blue}{-1} & = &1\color{blue}{-1} \\\Leftrightarrow &10x & = &0\\\Leftrightarrow & \color{red}{10}x & = &0\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{0}{10} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{-12}& = &12 \\\Leftrightarrow & 7x \color{red}{-12}\color{blue}{+12} & = &12\color{blue}{+12} \\\Leftrightarrow &7x & = &24\\\Leftrightarrow & \color{red}{7}x & = &24\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{24}{7} \\\Leftrightarrow & \color{green}{ x = \frac{24}{7} } & & \\ & V = \left\{ \frac{24}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{+14}& = &8 \\\Leftrightarrow & -5x \color{red}{+14}\color{blue}{-14} & = &8\color{blue}{-14} \\\Leftrightarrow &-5x & = &-6\\\Leftrightarrow & \color{red}{-5}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-6}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{-14}& = &-11 \\\Leftrightarrow & -11x \color{red}{-14}\color{blue}{+14} & = &-11\color{blue}{+14} \\\Leftrightarrow &-11x & = &3\\\Leftrightarrow & \color{red}{-11}x & = &3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{-15}& = &6 \\\Leftrightarrow & x \color{red}{-15}\color{blue}{+15} & = &6\color{blue}{+15} \\\Leftrightarrow &x & = &21\\\Leftrightarrow & \color{red}{}x & = &21\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 21 \\\Leftrightarrow & \color{green}{ x = 21 } & & \\ & V = \left\{ 21 \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{+10}& = &-3 \\\Leftrightarrow & -11x \color{red}{+10}\color{blue}{-10} & = &-3\color{blue}{-10} \\\Leftrightarrow &-11x & = &-13\\\Leftrightarrow & \color{red}{-11}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-13}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{13}{11} } & & \\ & V = \left\{ \frac{13}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{+6}& = &1 \\\Leftrightarrow & x \color{red}{+6}\color{blue}{-6} & = &1\color{blue}{-6} \\\Leftrightarrow &x & = &-5\\\Leftrightarrow & \color{red}{}x & = &-5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -5 \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{+15}& = &-15 \\\Leftrightarrow & 2x \color{red}{+15}\color{blue}{-15} & = &-15\color{blue}{-15} \\\Leftrightarrow &2x & = &-30\\\Leftrightarrow & \color{red}{2}x & = &-30\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-30}{2} \\\Leftrightarrow & \color{green}{ x = -15 } & & \\ & V = \left\{ -15 \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{-12}& = &11 \\\Leftrightarrow & 8x \color{red}{-12}\color{blue}{+12} & = &11\color{blue}{+12} \\\Leftrightarrow &8x & = &23\\\Leftrightarrow & \color{red}{8}x & = &23\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{23}{8} \\\Leftrightarrow & \color{green}{ x = \frac{23}{8} } & & \\ & V = \left\{ \frac{23}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{-3}& = &-10 \\\Leftrightarrow & -x \color{red}{-3}\color{blue}{+3} & = &-10\color{blue}{+3} \\\Leftrightarrow &-x & = &-7\\\Leftrightarrow & \color{red}{-}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-7}{-1} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)