Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{-14}& = &11 \\\Leftrightarrow & -4x \color{red}{-14}\color{blue}{+14} & = &11\color{blue}{+14} \\\Leftrightarrow &-4x & = &25\\\Leftrightarrow & \color{red}{-4}x & = &25\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{25}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{4} } & & \\ & V = \left\{ \frac{-25}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{+11}& = &5 \\\Leftrightarrow & -2x \color{red}{+11}\color{blue}{-11} & = &5\color{blue}{-11} \\\Leftrightarrow &-2x & = &-6\\\Leftrightarrow & \color{red}{-2}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-6}{-2} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{+2}& = &-12 \\\Leftrightarrow & -14x \color{red}{+2}\color{blue}{-2} & = &-12\color{blue}{-2} \\\Leftrightarrow &-14x & = &-14\\\Leftrightarrow & \color{red}{-14}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-14}{-14} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{+11}& = &-1 \\\Leftrightarrow & 13x \color{red}{+11}\color{blue}{-11} & = &-1\color{blue}{-11} \\\Leftrightarrow &13x & = &-12\\\Leftrightarrow & \color{red}{13}x & = &-12\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-12}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{+8}& = &7 \\\Leftrightarrow & 9x \color{red}{+8}\color{blue}{-8} & = &7\color{blue}{-8} \\\Leftrightarrow &9x & = &-1\\\Leftrightarrow & \color{red}{9}x & = &-1\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-1}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{9} } & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{+12}& = &-3 \\\Leftrightarrow & 2x \color{red}{+12}\color{blue}{-12} & = &-3\color{blue}{-12} \\\Leftrightarrow &2x & = &-15\\\Leftrightarrow & \color{red}{2}x & = &-15\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-15}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{2} } & & \\ & V = \left\{ \frac{-15}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{-6}& = &13 \\\Leftrightarrow & -x \color{red}{-6}\color{blue}{+6} & = &13\color{blue}{+6} \\\Leftrightarrow &-x & = &19\\\Leftrightarrow & \color{red}{-}x & = &19\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{19}{-1} \\\Leftrightarrow & \color{green}{ x = -19 } & & \\ & V = \left\{ -19 \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{+8}& = &-2 \\\Leftrightarrow & 12x \color{red}{+8}\color{blue}{-8} & = &-2\color{blue}{-8} \\\Leftrightarrow &12x & = &-10\\\Leftrightarrow & \color{red}{12}x & = &-10\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-10}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
9. \(\begin{align} & -9x \color{red}{-6}& = &10 \\\Leftrightarrow & -9x \color{red}{-6}\color{blue}{+6} & = &10\color{blue}{+6} \\\Leftrightarrow &-9x & = &16\\\Leftrightarrow & \color{red}{-9}x & = &16\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{16}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{9} } & & \\ & V = \left\{ \frac{-16}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{+15}& = &-12 \\\Leftrightarrow & 5x \color{red}{+15}\color{blue}{-15} & = &-12\color{blue}{-15} \\\Leftrightarrow &5x & = &-27\\\Leftrightarrow & \color{red}{5}x & = &-27\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-27}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{5} } & & \\ & V = \left\{ \frac{-27}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{+11}& = &-10 \\\Leftrightarrow & -6x \color{red}{+11}\color{blue}{-11} & = &-10\color{blue}{-11} \\\Leftrightarrow &-6x & = &-21\\\Leftrightarrow & \color{red}{-6}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-21}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{-7}& = &11 \\\Leftrightarrow & -15x \color{red}{-7}\color{blue}{+7} & = &11\color{blue}{+7} \\\Leftrightarrow &-15x & = &18\\\Leftrightarrow & \color{red}{-15}x & = &18\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{18}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)