Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 7x \color{red}{-11}& = &7 \\\Leftrightarrow & 7x \color{red}{-11}\color{blue}{+11} & = &7\color{blue}{+11} \\\Leftrightarrow &7x & = &18\\\Leftrightarrow & \color{red}{7}x & = &18\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{18}{7} \\\Leftrightarrow & \color{green}{ x = \frac{18}{7} } & & \\ & V = \left\{ \frac{18}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{-4}& = &-14 \\\Leftrightarrow & 10x \color{red}{-4}\color{blue}{+4} & = &-14\color{blue}{+4} \\\Leftrightarrow &10x & = &-10\\\Leftrightarrow & \color{red}{10}x & = &-10\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-10}{10} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{-12}& = &5 \\\Leftrightarrow & 8x \color{red}{-12}\color{blue}{+12} & = &5\color{blue}{+12} \\\Leftrightarrow &8x & = &17\\\Leftrightarrow & \color{red}{8}x & = &17\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{17}{8} \\\Leftrightarrow & \color{green}{ x = \frac{17}{8} } & & \\ & V = \left\{ \frac{17}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{+7}& = &-11 \\\Leftrightarrow & 9x \color{red}{+7}\color{blue}{-7} & = &-11\color{blue}{-7} \\\Leftrightarrow &9x & = &-18\\\Leftrightarrow & \color{red}{9}x & = &-18\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-18}{9} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{+1}& = &12 \\\Leftrightarrow & 13x \color{red}{+1}\color{blue}{-1} & = &12\color{blue}{-1} \\\Leftrightarrow &13x & = &11\\\Leftrightarrow & \color{red}{13}x & = &11\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{11}{13} \\\Leftrightarrow & \color{green}{ x = \frac{11}{13} } & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{+9}& = &12 \\\Leftrightarrow & 9x \color{red}{+9}\color{blue}{-9} & = &12\color{blue}{-9} \\\Leftrightarrow &9x & = &3\\\Leftrightarrow & \color{red}{9}x & = &3\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{3}{9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{+13}& = &7 \\\Leftrightarrow & 14x \color{red}{+13}\color{blue}{-13} & = &7\color{blue}{-13} \\\Leftrightarrow &14x & = &-6\\\Leftrightarrow & \color{red}{14}x & = &-6\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-6}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{-13}& = &12 \\\Leftrightarrow & -6x \color{red}{-13}\color{blue}{+13} & = &12\color{blue}{+13} \\\Leftrightarrow &-6x & = &25\\\Leftrightarrow & \color{red}{-6}x & = &25\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{25}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{6} } & & \\ & V = \left\{ \frac{-25}{6} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{-14}& = &-15 \\\Leftrightarrow & 9x \color{red}{-14}\color{blue}{+14} & = &-15\color{blue}{+14} \\\Leftrightarrow &9x & = &-1\\\Leftrightarrow & \color{red}{9}x & = &-1\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-1}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{9} } & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{+14}& = &-15 \\\Leftrightarrow & -5x \color{red}{+14}\color{blue}{-14} & = &-15\color{blue}{-14} \\\Leftrightarrow &-5x & = &-29\\\Leftrightarrow & \color{red}{-5}x & = &-29\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-29}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{29}{5} } & & \\ & V = \left\{ \frac{29}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{-10}& = &-1 \\\Leftrightarrow & -13x \color{red}{-10}\color{blue}{+10} & = &-1\color{blue}{+10} \\\Leftrightarrow &-13x & = &9\\\Leftrightarrow & \color{red}{-13}x & = &9\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{9}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{13} } & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{+15}& = &8 \\\Leftrightarrow & -3x \color{red}{+15}\color{blue}{-15} & = &8\color{blue}{-15} \\\Leftrightarrow &-3x & = &-7\\\Leftrightarrow & \color{red}{-3}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-7}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)