Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{+3}& = &-10 \\\Leftrightarrow & -6x \color{red}{+3}\color{blue}{-3} & = &-10\color{blue}{-3} \\\Leftrightarrow &-6x & = &-13\\\Leftrightarrow & \color{red}{-6}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-13}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{13}{6} } & & \\ & V = \left\{ \frac{13}{6} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{+10}& = &-1 \\\Leftrightarrow & -10x \color{red}{+10}\color{blue}{-10} & = &-1\color{blue}{-10} \\\Leftrightarrow &-10x & = &-11\\\Leftrightarrow & \color{red}{-10}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-11}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{11}{10} } & & \\ & V = \left\{ \frac{11}{10} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{+5}& = &-14 \\\Leftrightarrow & -2x \color{red}{+5}\color{blue}{-5} & = &-14\color{blue}{-5} \\\Leftrightarrow &-2x & = &-19\\\Leftrightarrow & \color{red}{-2}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-19}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{19}{2} } & & \\ & V = \left\{ \frac{19}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{+5}& = &1 \\\Leftrightarrow & 10x \color{red}{+5}\color{blue}{-5} & = &1\color{blue}{-5} \\\Leftrightarrow &10x & = &-4\\\Leftrightarrow & \color{red}{10}x & = &-4\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-4}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{+4}& = &-7 \\\Leftrightarrow & 8x \color{red}{+4}\color{blue}{-4} & = &-7\color{blue}{-4} \\\Leftrightarrow &8x & = &-11\\\Leftrightarrow & \color{red}{8}x & = &-11\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-11}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{8} } & & \\ & V = \left\{ \frac{-11}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{-8}& = &-3 \\\Leftrightarrow & -15x \color{red}{-8}\color{blue}{+8} & = &-3\color{blue}{+8} \\\Leftrightarrow &-15x & = &5\\\Leftrightarrow & \color{red}{-15}x & = &5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{+1}& = &-12 \\\Leftrightarrow & 3x \color{red}{+1}\color{blue}{-1} & = &-12\color{blue}{-1} \\\Leftrightarrow &3x & = &-13\\\Leftrightarrow & \color{red}{3}x & = &-13\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-13}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{3} } & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{+1}& = &3 \\\Leftrightarrow & -12x \color{red}{+1}\color{blue}{-1} & = &3\color{blue}{-1} \\\Leftrightarrow &-12x & = &2\\\Leftrightarrow & \color{red}{-12}x & = &2\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{2}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{-9}& = &-7 \\\Leftrightarrow & -14x \color{red}{-9}\color{blue}{+9} & = &-7\color{blue}{+9} \\\Leftrightarrow &-14x & = &2\\\Leftrightarrow & \color{red}{-14}x & = &2\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{2}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{+5}& = &11 \\\Leftrightarrow & 9x \color{red}{+5}\color{blue}{-5} & = &11\color{blue}{-5} \\\Leftrightarrow &9x & = &6\\\Leftrightarrow & \color{red}{9}x & = &6\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{6}{9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{+15}& = &-8 \\\Leftrightarrow & 9x \color{red}{+15}\color{blue}{-15} & = &-8\color{blue}{-15} \\\Leftrightarrow &9x & = &-23\\\Leftrightarrow & \color{red}{9}x & = &-23\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-23}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{9} } & & \\ & V = \left\{ \frac{-23}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{+6}& = &13 \\\Leftrightarrow & -11x \color{red}{+6}\color{blue}{-6} & = &13\color{blue}{-6} \\\Leftrightarrow &-11x & = &7\\\Leftrightarrow & \color{red}{-11}x & = &7\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{7}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)