Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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