Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{+11}& = &10 \\\Leftrightarrow & -7x \color{red}{+11}\color{blue}{-11} & = &10\color{blue}{-11} \\\Leftrightarrow &-7x & = &-1\\\Leftrightarrow & \color{red}{-7}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{+14}& = &-11 \\\Leftrightarrow & 2x \color{red}{+14}\color{blue}{-14} & = &-11\color{blue}{-14} \\\Leftrightarrow &2x & = &-25\\\Leftrightarrow & \color{red}{2}x & = &-25\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-25}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{2} } & & \\ & V = \left\{ \frac{-25}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{+6}& = &13 \\\Leftrightarrow & x \color{red}{+6}\color{blue}{-6} & = &13\color{blue}{-6} \\\Leftrightarrow &x & = &7\\\Leftrightarrow & \color{red}{}x & = &7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 7 \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{+11}& = &-14 \\\Leftrightarrow & -12x \color{red}{+11}\color{blue}{-11} & = &-14\color{blue}{-11} \\\Leftrightarrow &-12x & = &-25\\\Leftrightarrow & \color{red}{-12}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-25}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{25}{12} } & & \\ & V = \left\{ \frac{25}{12} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{+1}& = &6 \\\Leftrightarrow & 10x \color{red}{+1}\color{blue}{-1} & = &6\color{blue}{-1} \\\Leftrightarrow &10x & = &5\\\Leftrightarrow & \color{red}{10}x & = &5\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{5}{10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{-2}& = &-2 \\\Leftrightarrow & -9x \color{red}{-2}\color{blue}{+2} & = &-2\color{blue}{+2} \\\Leftrightarrow &-9x & = &0\\\Leftrightarrow & \color{red}{-9}x & = &0\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{0}{-9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{-14}& = &14 \\\Leftrightarrow & -11x \color{red}{-14}\color{blue}{+14} & = &14\color{blue}{+14} \\\Leftrightarrow &-11x & = &28\\\Leftrightarrow & \color{red}{-11}x & = &28\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{28}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-28}{11} } & & \\ & V = \left\{ \frac{-28}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{+15}& = &4 \\\Leftrightarrow & 6x \color{red}{+15}\color{blue}{-15} & = &4\color{blue}{-15} \\\Leftrightarrow &6x & = &-11\\\Leftrightarrow & \color{red}{6}x & = &-11\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-11}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{6} } & & \\ & V = \left\{ \frac{-11}{6} \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{-6}& = &14 \\\Leftrightarrow & -5x \color{red}{-6}\color{blue}{+6} & = &14\color{blue}{+6} \\\Leftrightarrow &-5x & = &20\\\Leftrightarrow & \color{red}{-5}x & = &20\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{20}{-5} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{-2}& = &2 \\\Leftrightarrow & -12x \color{red}{-2}\color{blue}{+2} & = &2\color{blue}{+2} \\\Leftrightarrow &-12x & = &4\\\Leftrightarrow & \color{red}{-12}x & = &4\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{4}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{+1}& = &5 \\\Leftrightarrow & -13x \color{red}{+1}\color{blue}{-1} & = &5\color{blue}{-1} \\\Leftrightarrow &-13x & = &4\\\Leftrightarrow & \color{red}{-13}x & = &4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{-5}& = &-11 \\\Leftrightarrow & 7x \color{red}{-5}\color{blue}{+5} & = &-11\color{blue}{+5} \\\Leftrightarrow &7x & = &-6\\\Leftrightarrow & \color{red}{7}x & = &-6\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-6}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)