Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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