Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 7x \color{red}{+11}& = &-8 \\\Leftrightarrow & 7x \color{red}{+11}\color{blue}{-11} & = &-8\color{blue}{-11} \\\Leftrightarrow &7x & = &-19\\\Leftrightarrow & \color{red}{7}x & = &-19\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-19}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{7} } & & \\ & V = \left\{ \frac{-19}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{+4}& = &14 \\\Leftrightarrow & -2x \color{red}{+4}\color{blue}{-4} & = &14\color{blue}{-4} \\\Leftrightarrow &-2x & = &10\\\Leftrightarrow & \color{red}{-2}x & = &10\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{10}{-2} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{-12}& = &6 \\\Leftrightarrow & 9x \color{red}{-12}\color{blue}{+12} & = &6\color{blue}{+12} \\\Leftrightarrow &9x & = &18\\\Leftrightarrow & \color{red}{9}x & = &18\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{18}{9} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{+7}& = &14 \\\Leftrightarrow & 6x \color{red}{+7}\color{blue}{-7} & = &14\color{blue}{-7} \\\Leftrightarrow &6x & = &7\\\Leftrightarrow & \color{red}{6}x & = &7\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{7}{6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{6} } & & \\ & V = \left\{ \frac{7}{6} \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{+8}& = &11 \\\Leftrightarrow & -15x \color{red}{+8}\color{blue}{-8} & = &11\color{blue}{-8} \\\Leftrightarrow &-15x & = &3\\\Leftrightarrow & \color{red}{-15}x & = &3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{-13}& = &-8 \\\Leftrightarrow & -14x \color{red}{-13}\color{blue}{+13} & = &-8\color{blue}{+13} \\\Leftrightarrow &-14x & = &5\\\Leftrightarrow & \color{red}{-14}x & = &5\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{5}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{14} } & & \\ & V = \left\{ \frac{-5}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{+12}& = &-12 \\\Leftrightarrow & -5x \color{red}{+12}\color{blue}{-12} & = &-12\color{blue}{-12} \\\Leftrightarrow &-5x & = &-24\\\Leftrightarrow & \color{red}{-5}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-24}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{24}{5} } & & \\ & V = \left\{ \frac{24}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{+5}& = &-8 \\\Leftrightarrow & 13x \color{red}{+5}\color{blue}{-5} & = &-8\color{blue}{-5} \\\Leftrightarrow &13x & = &-13\\\Leftrightarrow & \color{red}{13}x & = &-13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-13}{13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{-11}& = &14 \\\Leftrightarrow & x \color{red}{-11}\color{blue}{+11} & = &14\color{blue}{+11} \\\Leftrightarrow &x & = &25\\\Leftrightarrow & \color{red}{}x & = &25\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 25 \\\Leftrightarrow & \color{green}{ x = 25 } & & \\ & V = \left\{ 25 \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{+1}& = &13 \\\Leftrightarrow & -9x \color{red}{+1}\color{blue}{-1} & = &13\color{blue}{-1} \\\Leftrightarrow &-9x & = &12\\\Leftrightarrow & \color{red}{-9}x & = &12\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{12}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{-10}& = &-11 \\\Leftrightarrow & -7x \color{red}{-10}\color{blue}{+10} & = &-11\color{blue}{+10} \\\Leftrightarrow &-7x & = &-1\\\Leftrightarrow & \color{red}{-7}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{+4}& = &-7 \\\Leftrightarrow & 7x \color{red}{+4}\color{blue}{-4} & = &-7\color{blue}{-4} \\\Leftrightarrow &7x & = &-11\\\Leftrightarrow & \color{red}{7}x & = &-11\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-11}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{7} } & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)