Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{+5}& = &-7 \\\Leftrightarrow & 12x \color{red}{+5}\color{blue}{-5} & = &-7\color{blue}{-5} \\\Leftrightarrow &12x & = &-12\\\Leftrightarrow & \color{red}{12}x & = &-12\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-12}{12} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{-14}& = &10 \\\Leftrightarrow & 4x \color{red}{-14}\color{blue}{+14} & = &10\color{blue}{+14} \\\Leftrightarrow &4x & = &24\\\Leftrightarrow & \color{red}{4}x & = &24\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{24}{4} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{+12}& = &4 \\\Leftrightarrow & x \color{red}{+12}\color{blue}{-12} & = &4\color{blue}{-12} \\\Leftrightarrow &x & = &-8\\\Leftrightarrow & \color{red}{}x & = &-8\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -8 \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{+8}& = &14 \\\Leftrightarrow & -12x \color{red}{+8}\color{blue}{-8} & = &14\color{blue}{-8} \\\Leftrightarrow &-12x & = &6\\\Leftrightarrow & \color{red}{-12}x & = &6\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{6}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{-15}& = &5 \\\Leftrightarrow & -6x \color{red}{-15}\color{blue}{+15} & = &5\color{blue}{+15} \\\Leftrightarrow &-6x & = &20\\\Leftrightarrow & \color{red}{-6}x & = &20\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{20}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{3} } & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{+9}& = &5 \\\Leftrightarrow & -6x \color{red}{+9}\color{blue}{-9} & = &5\color{blue}{-9} \\\Leftrightarrow &-6x & = &-4\\\Leftrightarrow & \color{red}{-6}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-4}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{-2}& = &-7 \\\Leftrightarrow & 13x \color{red}{-2}\color{blue}{+2} & = &-7\color{blue}{+2} \\\Leftrightarrow &13x & = &-5\\\Leftrightarrow & \color{red}{13}x & = &-5\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-5}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{+1}& = &-7 \\\Leftrightarrow & 6x \color{red}{+1}\color{blue}{-1} & = &-7\color{blue}{-1} \\\Leftrightarrow &6x & = &-8\\\Leftrightarrow & \color{red}{6}x & = &-8\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-8}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{-14}& = &-8 \\\Leftrightarrow & -6x \color{red}{-14}\color{blue}{+14} & = &-8\color{blue}{+14} \\\Leftrightarrow &-6x & = &6\\\Leftrightarrow & \color{red}{-6}x & = &6\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{6}{-6} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{+7}& = &-3 \\\Leftrightarrow & 13x \color{red}{+7}\color{blue}{-7} & = &-3\color{blue}{-7} \\\Leftrightarrow &13x & = &-10\\\Leftrightarrow & \color{red}{13}x & = &-10\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-10}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{13} } & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{+15}& = &-5 \\\Leftrightarrow & 3x \color{red}{+15}\color{blue}{-15} & = &-5\color{blue}{-15} \\\Leftrightarrow &3x & = &-20\\\Leftrightarrow & \color{red}{3}x & = &-20\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-20}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{3} } & & \\ & V = \left\{ \frac{-20}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{-15}& = &-1 \\\Leftrightarrow & -5x \color{red}{-15}\color{blue}{+15} & = &-1\color{blue}{+15} \\\Leftrightarrow &-5x & = &14\\\Leftrightarrow & \color{red}{-5}x & = &14\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{14}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{5} } & & \\ & V = \left\{ \frac{-14}{5} \right\} & \\\end{align}\)