Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{-8}& = &-2 \\\Leftrightarrow & 12x \color{red}{-8}\color{blue}{+8} & = &-2\color{blue}{+8} \\\Leftrightarrow &12x & = &6\\\Leftrightarrow & \color{red}{12}x & = &6\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{6}{12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{+7}& = &-2 \\\Leftrightarrow & -x \color{red}{+7}\color{blue}{-7} & = &-2\color{blue}{-7} \\\Leftrightarrow &-x & = &-9\\\Leftrightarrow & \color{red}{-}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-9}{-1} \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{+14}& = &15 \\\Leftrightarrow & -8x \color{red}{+14}\color{blue}{-14} & = &15\color{blue}{-14} \\\Leftrightarrow &-8x & = &1\\\Leftrightarrow & \color{red}{-8}x & = &1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{-1}& = &4 \\\Leftrightarrow & -x \color{red}{-1}\color{blue}{+1} & = &4\color{blue}{+1} \\\Leftrightarrow &-x & = &5\\\Leftrightarrow & \color{red}{-}x & = &5\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{5}{-1} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{+1}& = &13 \\\Leftrightarrow & 13x \color{red}{+1}\color{blue}{-1} & = &13\color{blue}{-1} \\\Leftrightarrow &13x & = &12\\\Leftrightarrow & \color{red}{13}x & = &12\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{12}{13} \\\Leftrightarrow & \color{green}{ x = \frac{12}{13} } & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{-13}& = &-1 \\\Leftrightarrow & -13x \color{red}{-13}\color{blue}{+13} & = &-1\color{blue}{+13} \\\Leftrightarrow &-13x & = &12\\\Leftrightarrow & \color{red}{-13}x & = &12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{-2}& = &-14 \\\Leftrightarrow & 9x \color{red}{-2}\color{blue}{+2} & = &-14\color{blue}{+2} \\\Leftrightarrow &9x & = &-12\\\Leftrightarrow & \color{red}{9}x & = &-12\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-12}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{-11}& = &-1 \\\Leftrightarrow & -7x \color{red}{-11}\color{blue}{+11} & = &-1\color{blue}{+11} \\\Leftrightarrow &-7x & = &10\\\Leftrightarrow & \color{red}{-7}x & = &10\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{10}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{7} } & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{-1}& = &5 \\\Leftrightarrow & 13x \color{red}{-1}\color{blue}{+1} & = &5\color{blue}{+1} \\\Leftrightarrow &13x & = &6\\\Leftrightarrow & \color{red}{13}x & = &6\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{6}{13} \\\Leftrightarrow & \color{green}{ x = \frac{6}{13} } & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{-7}& = &12 \\\Leftrightarrow & -x \color{red}{-7}\color{blue}{+7} & = &12\color{blue}{+7} \\\Leftrightarrow &-x & = &19\\\Leftrightarrow & \color{red}{-}x & = &19\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{19}{-1} \\\Leftrightarrow & \color{green}{ x = -19 } & & \\ & V = \left\{ -19 \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{-9}& = &5 \\\Leftrightarrow & 14x \color{red}{-9}\color{blue}{+9} & = &5\color{blue}{+9} \\\Leftrightarrow &14x & = &14\\\Leftrightarrow & \color{red}{14}x & = &14\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{14}{14} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{-15}& = &15 \\\Leftrightarrow & 2x \color{red}{-15}\color{blue}{+15} & = &15\color{blue}{+15} \\\Leftrightarrow &2x & = &30\\\Leftrightarrow & \color{red}{2}x & = &30\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{30}{2} \\\Leftrightarrow & \color{green}{ x = 15 } & & \\ & V = \left\{ 15 \right\} & \\\end{align}\)