Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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