Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{+6}& = &15 \\\Leftrightarrow & -6x \color{red}{+6}\color{blue}{-6} & = &15\color{blue}{-6} \\\Leftrightarrow &-6x & = &9\\\Leftrightarrow & \color{red}{-6}x & = &9\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{9}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{-3}& = &12 \\\Leftrightarrow & -3x \color{red}{-3}\color{blue}{+3} & = &12\color{blue}{+3} \\\Leftrightarrow &-3x & = &15\\\Leftrightarrow & \color{red}{-3}x & = &15\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{15}{-3} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{+7}& = &7 \\\Leftrightarrow & -6x \color{red}{+7}\color{blue}{-7} & = &7\color{blue}{-7} \\\Leftrightarrow &-6x & = &0\\\Leftrightarrow & \color{red}{-6}x & = &0\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{0}{-6} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{-2}& = &-14 \\\Leftrightarrow & -5x \color{red}{-2}\color{blue}{+2} & = &-14\color{blue}{+2} \\\Leftrightarrow &-5x & = &-12\\\Leftrightarrow & \color{red}{-5}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-12}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{+7}& = &-6 \\\Leftrightarrow & 5x \color{red}{+7}\color{blue}{-7} & = &-6\color{blue}{-7} \\\Leftrightarrow &5x & = &-13\\\Leftrightarrow & \color{red}{5}x & = &-13\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-13}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{5} } & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{-4}& = &15 \\\Leftrightarrow & -6x \color{red}{-4}\color{blue}{+4} & = &15\color{blue}{+4} \\\Leftrightarrow &-6x & = &19\\\Leftrightarrow & \color{red}{-6}x & = &19\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{19}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{6} } & & \\ & V = \left\{ \frac{-19}{6} \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{-15}& = &-13 \\\Leftrightarrow & -12x \color{red}{-15}\color{blue}{+15} & = &-13\color{blue}{+15} \\\Leftrightarrow &-12x & = &2\\\Leftrightarrow & \color{red}{-12}x & = &2\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{2}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{+9}& = &8 \\\Leftrightarrow & 14x \color{red}{+9}\color{blue}{-9} & = &8\color{blue}{-9} \\\Leftrightarrow &14x & = &-1\\\Leftrightarrow & \color{red}{14}x & = &-1\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-1}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{14} } & & \\ & V = \left\{ \frac{-1}{14} \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{-1}& = &12 \\\Leftrightarrow & -12x \color{red}{-1}\color{blue}{+1} & = &12\color{blue}{+1} \\\Leftrightarrow &-12x & = &13\\\Leftrightarrow & \color{red}{-12}x & = &13\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{13}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{12} } & & \\ & V = \left\{ \frac{-13}{12} \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{-8}& = &14 \\\Leftrightarrow & -9x \color{red}{-8}\color{blue}{+8} & = &14\color{blue}{+8} \\\Leftrightarrow &-9x & = &22\\\Leftrightarrow & \color{red}{-9}x & = &22\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{22}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{9} } & & \\ & V = \left\{ \frac{-22}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{-14}& = &-15 \\\Leftrightarrow & -7x \color{red}{-14}\color{blue}{+14} & = &-15\color{blue}{+14} \\\Leftrightarrow &-7x & = &-1\\\Leftrightarrow & \color{red}{-7}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{-9}& = &12 \\\Leftrightarrow & -8x \color{red}{-9}\color{blue}{+9} & = &12\color{blue}{+9} \\\Leftrightarrow &-8x & = &21\\\Leftrightarrow & \color{red}{-8}x & = &21\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{21}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{8} } & & \\ & V = \left\{ \frac{-21}{8} \right\} & \\\end{align}\)