Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{-6}& = &10 \\\Leftrightarrow & -9x \color{red}{-6}\color{blue}{+6} & = &10\color{blue}{+6} \\\Leftrightarrow &-9x & = &16\\\Leftrightarrow & \color{red}{-9}x & = &16\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{16}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{9} } & & \\ & V = \left\{ \frac{-16}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{+15}& = &13 \\\Leftrightarrow & 15x \color{red}{+15}\color{blue}{-15} & = &13\color{blue}{-15} \\\Leftrightarrow &15x & = &-2\\\Leftrightarrow & \color{red}{15}x & = &-2\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-2}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{15} } & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{+13}& = &11 \\\Leftrightarrow & 15x \color{red}{+13}\color{blue}{-13} & = &11\color{blue}{-13} \\\Leftrightarrow &15x & = &-2\\\Leftrightarrow & \color{red}{15}x & = &-2\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-2}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{15} } & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{+1}& = &-13 \\\Leftrightarrow & 11x \color{red}{+1}\color{blue}{-1} & = &-13\color{blue}{-1} \\\Leftrightarrow &11x & = &-14\\\Leftrightarrow & \color{red}{11}x & = &-14\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-14}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{11} } & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{-12}& = &-13 \\\Leftrightarrow & 14x \color{red}{-12}\color{blue}{+12} & = &-13\color{blue}{+12} \\\Leftrightarrow &14x & = &-1\\\Leftrightarrow & \color{red}{14}x & = &-1\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-1}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{14} } & & \\ & V = \left\{ \frac{-1}{14} \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{-3}& = &-4 \\\Leftrightarrow & -x \color{red}{-3}\color{blue}{+3} & = &-4\color{blue}{+3} \\\Leftrightarrow &-x & = &-1\\\Leftrightarrow & \color{red}{-}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-1}{-1} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{+3}& = &3 \\\Leftrightarrow & 9x \color{red}{+3}\color{blue}{-3} & = &3\color{blue}{-3} \\\Leftrightarrow &9x & = &0\\\Leftrightarrow & \color{red}{9}x & = &0\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{0}{9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{+6}& = &2 \\\Leftrightarrow & -2x \color{red}{+6}\color{blue}{-6} & = &2\color{blue}{-6} \\\Leftrightarrow &-2x & = &-4\\\Leftrightarrow & \color{red}{-2}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-4}{-2} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{-1}& = &-13 \\\Leftrightarrow & 9x \color{red}{-1}\color{blue}{+1} & = &-13\color{blue}{+1} \\\Leftrightarrow &9x & = &-12\\\Leftrightarrow & \color{red}{9}x & = &-12\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-12}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{+11}& = &-15 \\\Leftrightarrow & -14x \color{red}{+11}\color{blue}{-11} & = &-15\color{blue}{-11} \\\Leftrightarrow &-14x & = &-26\\\Leftrightarrow & \color{red}{-14}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-26}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{13}{7} } & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{-14}& = &-1 \\\Leftrightarrow & 5x \color{red}{-14}\color{blue}{+14} & = &-1\color{blue}{+14} \\\Leftrightarrow &5x & = &13\\\Leftrightarrow & \color{red}{5}x & = &13\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{13}{5} \\\Leftrightarrow & \color{green}{ x = \frac{13}{5} } & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{+2}& = &-11 \\\Leftrightarrow & -9x \color{red}{+2}\color{blue}{-2} & = &-11\color{blue}{-2} \\\Leftrightarrow &-9x & = &-13\\\Leftrightarrow & \color{red}{-9}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-13}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{13}{9} } & & \\ & V = \left\{ \frac{13}{9} \right\} & \\\end{align}\)