Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{-5}& = &6 \\\Leftrightarrow & -15x \color{red}{-5}\color{blue}{+5} & = &6\color{blue}{+5} \\\Leftrightarrow &-15x & = &11\\\Leftrightarrow & \color{red}{-15}x & = &11\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{11}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{15} } & & \\ & V = \left\{ \frac{-11}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{-4}& = &6 \\\Leftrightarrow & -x \color{red}{-4}\color{blue}{+4} & = &6\color{blue}{+4} \\\Leftrightarrow &-x & = &10\\\Leftrightarrow & \color{red}{-}x & = &10\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{10}{-1} \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{+10}& = &2 \\\Leftrightarrow & 10x \color{red}{+10}\color{blue}{-10} & = &2\color{blue}{-10} \\\Leftrightarrow &10x & = &-8\\\Leftrightarrow & \color{red}{10}x & = &-8\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-8}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{-13}& = &9 \\\Leftrightarrow & 5x \color{red}{-13}\color{blue}{+13} & = &9\color{blue}{+13} \\\Leftrightarrow &5x & = &22\\\Leftrightarrow & \color{red}{5}x & = &22\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{22}{5} \\\Leftrightarrow & \color{green}{ x = \frac{22}{5} } & & \\ & V = \left\{ \frac{22}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{-4}& = &-10 \\\Leftrightarrow & 13x \color{red}{-4}\color{blue}{+4} & = &-10\color{blue}{+4} \\\Leftrightarrow &13x & = &-6\\\Leftrightarrow & \color{red}{13}x & = &-6\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-6}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{-13}& = &1 \\\Leftrightarrow & 6x \color{red}{-13}\color{blue}{+13} & = &1\color{blue}{+13} \\\Leftrightarrow &6x & = &14\\\Leftrightarrow & \color{red}{6}x & = &14\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{14}{6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{-9}& = &11 \\\Leftrightarrow & -2x \color{red}{-9}\color{blue}{+9} & = &11\color{blue}{+9} \\\Leftrightarrow &-2x & = &20\\\Leftrightarrow & \color{red}{-2}x & = &20\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{20}{-2} \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{-1}& = &14 \\\Leftrightarrow & x \color{red}{-1}\color{blue}{+1} & = &14\color{blue}{+1} \\\Leftrightarrow &x & = &15\\\Leftrightarrow & \color{red}{}x & = &15\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 15 \\\Leftrightarrow & \color{green}{ x = 15 } & & \\ & V = \left\{ 15 \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{-12}& = &3 \\\Leftrightarrow & 7x \color{red}{-12}\color{blue}{+12} & = &3\color{blue}{+12} \\\Leftrightarrow &7x & = &15\\\Leftrightarrow & \color{red}{7}x & = &15\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{15}{7} \\\Leftrightarrow & \color{green}{ x = \frac{15}{7} } & & \\ & V = \left\{ \frac{15}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{-1}& = &4 \\\Leftrightarrow & -6x \color{red}{-1}\color{blue}{+1} & = &4\color{blue}{+1} \\\Leftrightarrow &-6x & = &5\\\Leftrightarrow & \color{red}{-6}x & = &5\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{5}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{-1}& = &-12 \\\Leftrightarrow & -5x \color{red}{-1}\color{blue}{+1} & = &-12\color{blue}{+1} \\\Leftrightarrow &-5x & = &-11\\\Leftrightarrow & \color{red}{-5}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-11}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{11}{5} } & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{-15}& = &-15 \\\Leftrightarrow & -14x \color{red}{-15}\color{blue}{+15} & = &-15\color{blue}{+15} \\\Leftrightarrow &-14x & = &0\\\Leftrightarrow & \color{red}{-14}x & = &0\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{0}{-14} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)