Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{+7}& = &10 \\\Leftrightarrow & -13x \color{red}{+7}\color{blue}{-7} & = &10\color{blue}{-7} \\\Leftrightarrow &-13x & = &3\\\Leftrightarrow & \color{red}{-13}x & = &3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{+3}& = &-6 \\\Leftrightarrow & 8x \color{red}{+3}\color{blue}{-3} & = &-6\color{blue}{-3} \\\Leftrightarrow &8x & = &-9\\\Leftrightarrow & \color{red}{8}x & = &-9\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-9}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{8} } & & \\ & V = \left\{ \frac{-9}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{-3}& = &-7 \\\Leftrightarrow & 5x \color{red}{-3}\color{blue}{+3} & = &-7\color{blue}{+3} \\\Leftrightarrow &5x & = &-4\\\Leftrightarrow & \color{red}{5}x & = &-4\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-4}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{+10}& = &6 \\\Leftrightarrow & -9x \color{red}{+10}\color{blue}{-10} & = &6\color{blue}{-10} \\\Leftrightarrow &-9x & = &-4\\\Leftrightarrow & \color{red}{-9}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-4}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{9} } & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{+14}& = &-2 \\\Leftrightarrow & 12x \color{red}{+14}\color{blue}{-14} & = &-2\color{blue}{-14} \\\Leftrightarrow &12x & = &-16\\\Leftrightarrow & \color{red}{12}x & = &-16\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-16}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{-15}& = &12 \\\Leftrightarrow & -7x \color{red}{-15}\color{blue}{+15} & = &12\color{blue}{+15} \\\Leftrightarrow &-7x & = &27\\\Leftrightarrow & \color{red}{-7}x & = &27\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{27}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{7} } & & \\ & V = \left\{ \frac{-27}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{+6}& = &15 \\\Leftrightarrow & -3x \color{red}{+6}\color{blue}{-6} & = &15\color{blue}{-6} \\\Leftrightarrow &-3x & = &9\\\Leftrightarrow & \color{red}{-3}x & = &9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{9}{-3} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{-6}& = &5 \\\Leftrightarrow & -11x \color{red}{-6}\color{blue}{+6} & = &5\color{blue}{+6} \\\Leftrightarrow &-11x & = &11\\\Leftrightarrow & \color{red}{-11}x & = &11\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{11}{-11} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{-6}& = &9 \\\Leftrightarrow & 14x \color{red}{-6}\color{blue}{+6} & = &9\color{blue}{+6} \\\Leftrightarrow &14x & = &15\\\Leftrightarrow & \color{red}{14}x & = &15\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{15}{14} \\\Leftrightarrow & \color{green}{ x = \frac{15}{14} } & & \\ & V = \left\{ \frac{15}{14} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{+11}& = &2 \\\Leftrightarrow & 7x \color{red}{+11}\color{blue}{-11} & = &2\color{blue}{-11} \\\Leftrightarrow &7x & = &-9\\\Leftrightarrow & \color{red}{7}x & = &-9\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-9}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{+4}& = &14 \\\Leftrightarrow & 15x \color{red}{+4}\color{blue}{-4} & = &14\color{blue}{-4} \\\Leftrightarrow &15x & = &10\\\Leftrightarrow & \color{red}{15}x & = &10\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{10}{15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{-15}& = &-2 \\\Leftrightarrow & 2x \color{red}{-15}\color{blue}{+15} & = &-2\color{blue}{+15} \\\Leftrightarrow &2x & = &13\\\Leftrightarrow & \color{red}{2}x & = &13\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{13}{2} \\\Leftrightarrow & \color{green}{ x = \frac{13}{2} } & & \\ & V = \left\{ \frac{13}{2} \right\} & \\\end{align}\)