Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & x \color{red}{-14}& = &14 \\\Leftrightarrow & x \color{red}{-14}\color{blue}{+14} & = &14\color{blue}{+14} \\\Leftrightarrow &x & = &28\\\Leftrightarrow & \color{red}{}x & = &28\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 28 \\\Leftrightarrow & \color{green}{ x = 28 } & & \\ & V = \left\{ 28 \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{+10}& = &-1 \\\Leftrightarrow & 4x \color{red}{+10}\color{blue}{-10} & = &-1\color{blue}{-10} \\\Leftrightarrow &4x & = &-11\\\Leftrightarrow & \color{red}{4}x & = &-11\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-11}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{4} } & & \\ & V = \left\{ \frac{-11}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{-2}& = &7 \\\Leftrightarrow & -11x \color{red}{-2}\color{blue}{+2} & = &7\color{blue}{+2} \\\Leftrightarrow &-11x & = &9\\\Leftrightarrow & \color{red}{-11}x & = &9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{11} } & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{-15}& = &-6 \\\Leftrightarrow & -13x \color{red}{-15}\color{blue}{+15} & = &-6\color{blue}{+15} \\\Leftrightarrow &-13x & = &9\\\Leftrightarrow & \color{red}{-13}x & = &9\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{9}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{13} } & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{+13}& = &-2 \\\Leftrightarrow & 9x \color{red}{+13}\color{blue}{-13} & = &-2\color{blue}{-13} \\\Leftrightarrow &9x & = &-15\\\Leftrightarrow & \color{red}{9}x & = &-15\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-15}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{+6}& = &-12 \\\Leftrightarrow & -9x \color{red}{+6}\color{blue}{-6} & = &-12\color{blue}{-6} \\\Leftrightarrow &-9x & = &-18\\\Leftrightarrow & \color{red}{-9}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-18}{-9} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{+8}& = &4 \\\Leftrightarrow & 11x \color{red}{+8}\color{blue}{-8} & = &4\color{blue}{-8} \\\Leftrightarrow &11x & = &-4\\\Leftrightarrow & \color{red}{11}x & = &-4\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-4}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{+9}& = &-13 \\\Leftrightarrow & 10x \color{red}{+9}\color{blue}{-9} & = &-13\color{blue}{-9} \\\Leftrightarrow &10x & = &-22\\\Leftrightarrow & \color{red}{10}x & = &-22\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-22}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{5} } & & \\ & V = \left\{ \frac{-11}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{-4}& = &-10 \\\Leftrightarrow & -14x \color{red}{-4}\color{blue}{+4} & = &-10\color{blue}{+4} \\\Leftrightarrow &-14x & = &-6\\\Leftrightarrow & \color{red}{-14}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-6}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{-9}& = &-4 \\\Leftrightarrow & -13x \color{red}{-9}\color{blue}{+9} & = &-4\color{blue}{+9} \\\Leftrightarrow &-13x & = &5\\\Leftrightarrow & \color{red}{-13}x & = &5\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{5}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{+11}& = &-8 \\\Leftrightarrow & -11x \color{red}{+11}\color{blue}{-11} & = &-8\color{blue}{-11} \\\Leftrightarrow &-11x & = &-19\\\Leftrightarrow & \color{red}{-11}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-19}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{19}{11} } & & \\ & V = \left\{ \frac{19}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{-9}& = &10 \\\Leftrightarrow & -7x \color{red}{-9}\color{blue}{+9} & = &10\color{blue}{+9} \\\Leftrightarrow &-7x & = &19\\\Leftrightarrow & \color{red}{-7}x & = &19\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{19}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{7} } & & \\ & V = \left\{ \frac{-19}{7} \right\} & \\\end{align}\)