Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{-8}& = &-10 \\\Leftrightarrow & -9x \color{red}{-8}\color{blue}{+8} & = &-10\color{blue}{+8} \\\Leftrightarrow &-9x & = &-2\\\Leftrightarrow & \color{red}{-9}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{9} } & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{+15}& = &-1 \\\Leftrightarrow & 15x \color{red}{+15}\color{blue}{-15} & = &-1\color{blue}{-15} \\\Leftrightarrow &15x & = &-16\\\Leftrightarrow & \color{red}{15}x & = &-16\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-16}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{15} } & & \\ & V = \left\{ \frac{-16}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{+5}& = &4 \\\Leftrightarrow & 3x \color{red}{+5}\color{blue}{-5} & = &4\color{blue}{-5} \\\Leftrightarrow &3x & = &-1\\\Leftrightarrow & \color{red}{3}x & = &-1\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-1}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{+13}& = &1 \\\Leftrightarrow & -4x \color{red}{+13}\color{blue}{-13} & = &1\color{blue}{-13} \\\Leftrightarrow &-4x & = &-12\\\Leftrightarrow & \color{red}{-4}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-12}{-4} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{-6}& = &1 \\\Leftrightarrow & -13x \color{red}{-6}\color{blue}{+6} & = &1\color{blue}{+6} \\\Leftrightarrow &-13x & = &7\\\Leftrightarrow & \color{red}{-13}x & = &7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{13} } & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{+2}& = &1 \\\Leftrightarrow & -9x \color{red}{+2}\color{blue}{-2} & = &1\color{blue}{-2} \\\Leftrightarrow &-9x & = &-1\\\Leftrightarrow & \color{red}{-9}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-1}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{+4}& = &-10 \\\Leftrightarrow & 4x \color{red}{+4}\color{blue}{-4} & = &-10\color{blue}{-4} \\\Leftrightarrow &4x & = &-14\\\Leftrightarrow & \color{red}{4}x & = &-14\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-14}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{+13}& = &-6 \\\Leftrightarrow & -13x \color{red}{+13}\color{blue}{-13} & = &-6\color{blue}{-13} \\\Leftrightarrow &-13x & = &-19\\\Leftrightarrow & \color{red}{-13}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-19}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{19}{13} } & & \\ & V = \left\{ \frac{19}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{-12}& = &-14 \\\Leftrightarrow & 4x \color{red}{-12}\color{blue}{+12} & = &-14\color{blue}{+12} \\\Leftrightarrow &4x & = &-2\\\Leftrightarrow & \color{red}{4}x & = &-2\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-2}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{+13}& = &5 \\\Leftrightarrow & 6x \color{red}{+13}\color{blue}{-13} & = &5\color{blue}{-13} \\\Leftrightarrow &6x & = &-8\\\Leftrightarrow & \color{red}{6}x & = &-8\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-8}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{+15}& = &6 \\\Leftrightarrow & -10x \color{red}{+15}\color{blue}{-15} & = &6\color{blue}{-15} \\\Leftrightarrow &-10x & = &-9\\\Leftrightarrow & \color{red}{-10}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-9}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{9}{10} } & & \\ & V = \left\{ \frac{9}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{-5}& = &-15 \\\Leftrightarrow & 8x \color{red}{-5}\color{blue}{+5} & = &-15\color{blue}{+5} \\\Leftrightarrow &8x & = &-10\\\Leftrightarrow & \color{red}{8}x & = &-10\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-10}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)