Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{+6}& = &-5 \\\Leftrightarrow & 12x \color{red}{+6}\color{blue}{-6} & = &-5\color{blue}{-6} \\\Leftrightarrow &12x & = &-11\\\Leftrightarrow & \color{red}{12}x & = &-11\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-11}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{12} } & & \\ & V = \left\{ \frac{-11}{12} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{+6}& = &-11 \\\Leftrightarrow & 6x \color{red}{+6}\color{blue}{-6} & = &-11\color{blue}{-6} \\\Leftrightarrow &6x & = &-17\\\Leftrightarrow & \color{red}{6}x & = &-17\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-17}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{6} } & & \\ & V = \left\{ \frac{-17}{6} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{+6}& = &6 \\\Leftrightarrow & 14x \color{red}{+6}\color{blue}{-6} & = &6\color{blue}{-6} \\\Leftrightarrow &14x & = &0\\\Leftrightarrow & \color{red}{14}x & = &0\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{0}{14} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{-9}& = &1 \\\Leftrightarrow & -4x \color{red}{-9}\color{blue}{+9} & = &1\color{blue}{+9} \\\Leftrightarrow &-4x & = &10\\\Leftrightarrow & \color{red}{-4}x & = &10\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{10}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{+13}& = &7 \\\Leftrightarrow & 8x \color{red}{+13}\color{blue}{-13} & = &7\color{blue}{-13} \\\Leftrightarrow &8x & = &-6\\\Leftrightarrow & \color{red}{8}x & = &-6\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-6}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{+4}& = &8 \\\Leftrightarrow & -12x \color{red}{+4}\color{blue}{-4} & = &8\color{blue}{-4} \\\Leftrightarrow &-12x & = &4\\\Leftrightarrow & \color{red}{-12}x & = &4\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{4}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{-15}& = &15 \\\Leftrightarrow & -4x \color{red}{-15}\color{blue}{+15} & = &15\color{blue}{+15} \\\Leftrightarrow &-4x & = &30\\\Leftrightarrow & \color{red}{-4}x & = &30\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{30}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{2} } & & \\ & V = \left\{ \frac{-15}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{-7}& = &-6 \\\Leftrightarrow & x \color{red}{-7}\color{blue}{+7} & = &-6\color{blue}{+7} \\\Leftrightarrow &x & = &1\\\Leftrightarrow & \color{red}{}x & = &1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 1 \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{-5}& = &-6 \\\Leftrightarrow & -4x \color{red}{-5}\color{blue}{+5} & = &-6\color{blue}{+5} \\\Leftrightarrow &-4x & = &-1\\\Leftrightarrow & \color{red}{-4}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{-2}& = &15 \\\Leftrightarrow & 3x \color{red}{-2}\color{blue}{+2} & = &15\color{blue}{+2} \\\Leftrightarrow &3x & = &17\\\Leftrightarrow & \color{red}{3}x & = &17\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{17}{3} \\\Leftrightarrow & \color{green}{ x = \frac{17}{3} } & & \\ & V = \left\{ \frac{17}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{+6}& = &11 \\\Leftrightarrow & x \color{red}{+6}\color{blue}{-6} & = &11\color{blue}{-6} \\\Leftrightarrow &x & = &5\\\Leftrightarrow & \color{red}{}x & = &5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 5 \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{-2}& = &11 \\\Leftrightarrow & -x \color{red}{-2}\color{blue}{+2} & = &11\color{blue}{+2} \\\Leftrightarrow &-x & = &13\\\Leftrightarrow & \color{red}{-}x & = &13\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{13}{-1} \\\Leftrightarrow & \color{green}{ x = -13 } & & \\ & V = \left\{ -13 \right\} & \\\end{align}\)