Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{+2}& = &-9 \\\Leftrightarrow & -9x \color{red}{+2}\color{blue}{-2} & = &-9\color{blue}{-2} \\\Leftrightarrow &-9x & = &-11\\\Leftrightarrow & \color{red}{-9}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-11}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{11}{9} } & & \\ & V = \left\{ \frac{11}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{+4}& = &15 \\\Leftrightarrow & -9x \color{red}{+4}\color{blue}{-4} & = &15\color{blue}{-4} \\\Leftrightarrow &-9x & = &11\\\Leftrightarrow & \color{red}{-9}x & = &11\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{11}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{9} } & & \\ & V = \left\{ \frac{-11}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{+13}& = &-10 \\\Leftrightarrow & 13x \color{red}{+13}\color{blue}{-13} & = &-10\color{blue}{-13} \\\Leftrightarrow &13x & = &-23\\\Leftrightarrow & \color{red}{13}x & = &-23\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-23}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{13} } & & \\ & V = \left\{ \frac{-23}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{+9}& = &-13 \\\Leftrightarrow & -13x \color{red}{+9}\color{blue}{-9} & = &-13\color{blue}{-9} \\\Leftrightarrow &-13x & = &-22\\\Leftrightarrow & \color{red}{-13}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-22}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{22}{13} } & & \\ & V = \left\{ \frac{22}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{+6}& = &1 \\\Leftrightarrow & 10x \color{red}{+6}\color{blue}{-6} & = &1\color{blue}{-6} \\\Leftrightarrow &10x & = &-5\\\Leftrightarrow & \color{red}{10}x & = &-5\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-5}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{-4}& = &-5 \\\Leftrightarrow & -2x \color{red}{-4}\color{blue}{+4} & = &-5\color{blue}{+4} \\\Leftrightarrow &-2x & = &-1\\\Leftrightarrow & \color{red}{-2}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-1}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{+12}& = &11 \\\Leftrightarrow & -11x \color{red}{+12}\color{blue}{-12} & = &11\color{blue}{-12} \\\Leftrightarrow &-11x & = &-1\\\Leftrightarrow & \color{red}{-11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{+13}& = &-5 \\\Leftrightarrow & 11x \color{red}{+13}\color{blue}{-13} & = &-5\color{blue}{-13} \\\Leftrightarrow &11x & = &-18\\\Leftrightarrow & \color{red}{11}x & = &-18\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-18}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{11} } & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{+10}& = &14 \\\Leftrightarrow & 5x \color{red}{+10}\color{blue}{-10} & = &14\color{blue}{-10} \\\Leftrightarrow &5x & = &4\\\Leftrightarrow & \color{red}{5}x & = &4\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{4}{5} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{+8}& = &9 \\\Leftrightarrow & -9x \color{red}{+8}\color{blue}{-8} & = &9\color{blue}{-8} \\\Leftrightarrow &-9x & = &1\\\Leftrightarrow & \color{red}{-9}x & = &1\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{1}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{9} } & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{-1}& = &2 \\\Leftrightarrow & 4x \color{red}{-1}\color{blue}{+1} & = &2\color{blue}{+1} \\\Leftrightarrow &4x & = &3\\\Leftrightarrow & \color{red}{4}x & = &3\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{3}{4} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{-9}& = &-5 \\\Leftrightarrow & -13x \color{red}{-9}\color{blue}{+9} & = &-5\color{blue}{+9} \\\Leftrightarrow &-13x & = &4\\\Leftrightarrow & \color{red}{-13}x & = &4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)