Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{+13}& = & 13 \color{red}{ -13x } \\\Leftrightarrow & x \color{red}{+13}\color{blue}{-13+13x } & = & 13 \color{red}{ -13x }\color{blue}{-13+13x } \\\Leftrightarrow & x \color{blue}{+13x } & = & 13 \color{blue}{-13} \\\Leftrightarrow &14x & = &0\\\Leftrightarrow & \color{red}{14}x & = &0\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{0}{14} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{-5}& = & 4 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-5}\color{blue}{+5-9x } & = & 4 \color{red}{ +9x }\color{blue}{+5-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & 4 \color{blue}{+5} \\\Leftrightarrow &5x & = &9\\\Leftrightarrow & \color{red}{5}x & = &9\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{9}{5} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{+15}& = & -12 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{+15}\color{blue}{-15+8x } & = & -12 \color{red}{ -8x }\color{blue}{-15+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & -12 \color{blue}{-15} \\\Leftrightarrow &17x & = &-27\\\Leftrightarrow & \color{red}{17}x & = &-27\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-27}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{17} } & & \\ & V = \left\{ \frac{-27}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{-12}& = & -2 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-12}\color{blue}{+12+2x } & = & -2 \color{red}{ -2x }\color{blue}{+12+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -2 \color{blue}{+12} \\\Leftrightarrow &17x & = &10\\\Leftrightarrow & \color{red}{17}x & = &10\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{10}{17} \\\Leftrightarrow & \color{green}{ x = \frac{10}{17} } & & \\ & V = \left\{ \frac{10}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{+14}& = & 9 \color{red}{ +2x } \\\Leftrightarrow & 9x \color{red}{+14}\color{blue}{-14-2x } & = & 9 \color{red}{ +2x }\color{blue}{-14-2x } \\\Leftrightarrow & 9x \color{blue}{-2x } & = & 9 \color{blue}{-14} \\\Leftrightarrow &7x & = &-5\\\Leftrightarrow & \color{red}{7}x & = &-5\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-5}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{-5}& = & -7 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{-5}\color{blue}{+5-5x } & = & -7 \color{red}{ +5x }\color{blue}{+5-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & -7 \color{blue}{+5} \\\Leftrightarrow &-9x & = &-2\\\Leftrightarrow & \color{red}{-9}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{9} } & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{-3}& = & -8 \color{red}{ +3x } \\\Leftrightarrow & 10x \color{red}{-3}\color{blue}{+3-3x } & = & -8 \color{red}{ +3x }\color{blue}{+3-3x } \\\Leftrightarrow & 10x \color{blue}{-3x } & = & -8 \color{blue}{+3} \\\Leftrightarrow &7x & = &-5\\\Leftrightarrow & \color{red}{7}x & = &-5\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-5}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{+2}& = & -4 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{+2}\color{blue}{-2-9x } & = & -4 \color{red}{ +9x }\color{blue}{-2-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & -4 \color{blue}{-2} \\\Leftrightarrow &-20x & = &-6\\\Leftrightarrow & \color{red}{-20}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-6}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{3}{10} } & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{-9}& = & 15 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-9}\color{blue}{+9+13x } & = & 15 \color{red}{ -13x }\color{blue}{+9+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 15 \color{blue}{+9} \\\Leftrightarrow &27x & = &24\\\Leftrightarrow & \color{red}{27}x & = &24\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{24}{27} \\\Leftrightarrow & \color{green}{ x = \frac{8}{9} } & & \\ & V = \left\{ \frac{8}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{-2}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-2}\color{blue}{+2-x } & = & -6 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -6 \color{blue}{+2} \\\Leftrightarrow &-4x & = &-4\\\Leftrightarrow & \color{red}{-4}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-4}{-4} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{+4}& = & -11 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{+4}\color{blue}{-4+5x } & = & -11 \color{red}{ -5x }\color{blue}{-4+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & -11 \color{blue}{-4} \\\Leftrightarrow &8x & = &-15\\\Leftrightarrow & \color{red}{8}x & = &-15\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-15}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{8} } & & \\ & V = \left\{ \frac{-15}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{-1}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{-1}\color{blue}{+1-x } & = & -12 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & -12 \color{blue}{+1} \\\Leftrightarrow &6x & = &-11\\\Leftrightarrow & \color{red}{6}x & = &-11\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-11}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{6} } & & \\ & V = \left\{ \frac{-11}{6} \right\} & \\\end{align}\)