Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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