Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{-14}& = &-11 \\\Leftrightarrow & -6x \color{red}{-14}\color{blue}{+14} & = &-11\color{blue}{+14} \\\Leftrightarrow &-6x & = &3\\\Leftrightarrow & \color{red}{-6}x & = &3\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{3}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{+13}& = &1 \\\Leftrightarrow & 2x \color{red}{+13}\color{blue}{-13} & = &1\color{blue}{-13} \\\Leftrightarrow &2x & = &-12\\\Leftrightarrow & \color{red}{2}x & = &-12\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-12}{2} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{+10}& = &7 \\\Leftrightarrow & 13x \color{red}{+10}\color{blue}{-10} & = &7\color{blue}{-10} \\\Leftrightarrow &13x & = &-3\\\Leftrightarrow & \color{red}{13}x & = &-3\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-3}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{-5}& = &-5 \\\Leftrightarrow & -x \color{red}{-5}\color{blue}{+5} & = &-5\color{blue}{+5} \\\Leftrightarrow &-x & = &0\\\Leftrightarrow & \color{red}{-}x & = &0\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{0}{-1} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{+14}& = &7 \\\Leftrightarrow & -2x \color{red}{+14}\color{blue}{-14} & = &7\color{blue}{-14} \\\Leftrightarrow &-2x & = &-7\\\Leftrightarrow & \color{red}{-2}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-7}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{+6}& = &-10 \\\Leftrightarrow & 4x \color{red}{+6}\color{blue}{-6} & = &-10\color{blue}{-6} \\\Leftrightarrow &4x & = &-16\\\Leftrightarrow & \color{red}{4}x & = &-16\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-16}{4} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{-4}& = &-3 \\\Leftrightarrow & -4x \color{red}{-4}\color{blue}{+4} & = &-3\color{blue}{+4} \\\Leftrightarrow &-4x & = &1\\\Leftrightarrow & \color{red}{-4}x & = &1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{+10}& = &-10 \\\Leftrightarrow & 3x \color{red}{+10}\color{blue}{-10} & = &-10\color{blue}{-10} \\\Leftrightarrow &3x & = &-20\\\Leftrightarrow & \color{red}{3}x & = &-20\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-20}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{3} } & & \\ & V = \left\{ \frac{-20}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{-12}& = &-11 \\\Leftrightarrow & -10x \color{red}{-12}\color{blue}{+12} & = &-11\color{blue}{+12} \\\Leftrightarrow &-10x & = &1\\\Leftrightarrow & \color{red}{-10}x & = &1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{+14}& = &12 \\\Leftrightarrow & 14x \color{red}{+14}\color{blue}{-14} & = &12\color{blue}{-14} \\\Leftrightarrow &14x & = &-2\\\Leftrightarrow & \color{red}{14}x & = &-2\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-2}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{+8}& = &6 \\\Leftrightarrow & -4x \color{red}{+8}\color{blue}{-8} & = &6\color{blue}{-8} \\\Leftrightarrow &-4x & = &-2\\\Leftrightarrow & \color{red}{-4}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{-14}& = &14 \\\Leftrightarrow & -x \color{red}{-14}\color{blue}{+14} & = &14\color{blue}{+14} \\\Leftrightarrow &-x & = &28\\\Leftrightarrow & \color{red}{-}x & = &28\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{28}{-1} \\\Leftrightarrow & \color{green}{ x = -28 } & & \\ & V = \left\{ -28 \right\} & \\\end{align}\)