Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{-13}& = &11 \\\Leftrightarrow & 2x \color{red}{-13}\color{blue}{+13} & = &11\color{blue}{+13} \\\Leftrightarrow &2x & = &24\\\Leftrightarrow & \color{red}{2}x & = &24\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{24}{2} \\\Leftrightarrow & \color{green}{ x = 12 } & & \\ & V = \left\{ 12 \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{-10}& = &2 \\\Leftrightarrow & -13x \color{red}{-10}\color{blue}{+10} & = &2\color{blue}{+10} \\\Leftrightarrow &-13x & = &12\\\Leftrightarrow & \color{red}{-13}x & = &12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{+13}& = &4 \\\Leftrightarrow & 13x \color{red}{+13}\color{blue}{-13} & = &4\color{blue}{-13} \\\Leftrightarrow &13x & = &-9\\\Leftrightarrow & \color{red}{13}x & = &-9\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-9}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{13} } & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{-4}& = &-6 \\\Leftrightarrow & -3x \color{red}{-4}\color{blue}{+4} & = &-6\color{blue}{+4} \\\Leftrightarrow &-3x & = &-2\\\Leftrightarrow & \color{red}{-3}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{+10}& = &-13 \\\Leftrightarrow & -14x \color{red}{+10}\color{blue}{-10} & = &-13\color{blue}{-10} \\\Leftrightarrow &-14x & = &-23\\\Leftrightarrow & \color{red}{-14}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-23}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{23}{14} } & & \\ & V = \left\{ \frac{23}{14} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{-11}& = &-12 \\\Leftrightarrow & 9x \color{red}{-11}\color{blue}{+11} & = &-12\color{blue}{+11} \\\Leftrightarrow &9x & = &-1\\\Leftrightarrow & \color{red}{9}x & = &-1\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-1}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{9} } & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{+9}& = &7 \\\Leftrightarrow & -3x \color{red}{+9}\color{blue}{-9} & = &7\color{blue}{-9} \\\Leftrightarrow &-3x & = &-2\\\Leftrightarrow & \color{red}{-3}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{+3}& = &9 \\\Leftrightarrow & 13x \color{red}{+3}\color{blue}{-3} & = &9\color{blue}{-3} \\\Leftrightarrow &13x & = &6\\\Leftrightarrow & \color{red}{13}x & = &6\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{6}{13} \\\Leftrightarrow & \color{green}{ x = \frac{6}{13} } & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{+2}& = &-3 \\\Leftrightarrow & -2x \color{red}{+2}\color{blue}{-2} & = &-3\color{blue}{-2} \\\Leftrightarrow &-2x & = &-5\\\Leftrightarrow & \color{red}{-2}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-5}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{+8}& = &-15 \\\Leftrightarrow & 9x \color{red}{+8}\color{blue}{-8} & = &-15\color{blue}{-8} \\\Leftrightarrow &9x & = &-23\\\Leftrightarrow & \color{red}{9}x & = &-23\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-23}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{9} } & & \\ & V = \left\{ \frac{-23}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{+6}& = &-15 \\\Leftrightarrow & 9x \color{red}{+6}\color{blue}{-6} & = &-15\color{blue}{-6} \\\Leftrightarrow &9x & = &-21\\\Leftrightarrow & \color{red}{9}x & = &-21\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-21}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{+15}& = &1 \\\Leftrightarrow & x \color{red}{+15}\color{blue}{-15} & = &1\color{blue}{-15} \\\Leftrightarrow &x & = &-14\\\Leftrightarrow & \color{red}{}x & = &-14\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -14 \\\Leftrightarrow & \color{green}{ x = -14 } & & \\ & V = \left\{ -14 \right\} & \\\end{align}\)