Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 7x \color{red}{+1}& = &-6 \\\Leftrightarrow & 7x \color{red}{+1}\color{blue}{-1} & = &-6\color{blue}{-1} \\\Leftrightarrow &7x & = &-7\\\Leftrightarrow & \color{red}{7}x & = &-7\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-7}{7} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{-13}& = &7 \\\Leftrightarrow & -2x \color{red}{-13}\color{blue}{+13} & = &7\color{blue}{+13} \\\Leftrightarrow &-2x & = &20\\\Leftrightarrow & \color{red}{-2}x & = &20\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{20}{-2} \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{+4}& = &-8 \\\Leftrightarrow & -15x \color{red}{+4}\color{blue}{-4} & = &-8\color{blue}{-4} \\\Leftrightarrow &-15x & = &-12\\\Leftrightarrow & \color{red}{-15}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{+5}& = &1 \\\Leftrightarrow & -13x \color{red}{+5}\color{blue}{-5} & = &1\color{blue}{-5} \\\Leftrightarrow &-13x & = &-4\\\Leftrightarrow & \color{red}{-13}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{+11}& = &14 \\\Leftrightarrow & 14x \color{red}{+11}\color{blue}{-11} & = &14\color{blue}{-11} \\\Leftrightarrow &14x & = &3\\\Leftrightarrow & \color{red}{14}x & = &3\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{3}{14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{14} } & & \\ & V = \left\{ \frac{3}{14} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{-5}& = &13 \\\Leftrightarrow & -9x \color{red}{-5}\color{blue}{+5} & = &13\color{blue}{+5} \\\Leftrightarrow &-9x & = &18\\\Leftrightarrow & \color{red}{-9}x & = &18\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{18}{-9} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{-6}& = &5 \\\Leftrightarrow & 2x \color{red}{-6}\color{blue}{+6} & = &5\color{blue}{+6} \\\Leftrightarrow &2x & = &11\\\Leftrightarrow & \color{red}{2}x & = &11\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{11}{2} \\\Leftrightarrow & \color{green}{ x = \frac{11}{2} } & & \\ & V = \left\{ \frac{11}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{+9}& = &10 \\\Leftrightarrow & 2x \color{red}{+9}\color{blue}{-9} & = &10\color{blue}{-9} \\\Leftrightarrow &2x & = &1\\\Leftrightarrow & \color{red}{2}x & = &1\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{1}{2} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{+1}& = &4 \\\Leftrightarrow & -2x \color{red}{+1}\color{blue}{-1} & = &4\color{blue}{-1} \\\Leftrightarrow &-2x & = &3\\\Leftrightarrow & \color{red}{-2}x & = &3\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{3}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{+15}& = &15 \\\Leftrightarrow & 7x \color{red}{+15}\color{blue}{-15} & = &15\color{blue}{-15} \\\Leftrightarrow &7x & = &0\\\Leftrightarrow & \color{red}{7}x & = &0\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{0}{7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{-6}& = &-13 \\\Leftrightarrow & -7x \color{red}{-6}\color{blue}{+6} & = &-13\color{blue}{+6} \\\Leftrightarrow &-7x & = &-7\\\Leftrightarrow & \color{red}{-7}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-7}{-7} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{+13}& = &14 \\\Leftrightarrow & -8x \color{red}{+13}\color{blue}{-13} & = &14\color{blue}{-13} \\\Leftrightarrow &-8x & = &1\\\Leftrightarrow & \color{red}{-8}x & = &1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)