Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{+11}& = & 13 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{+11}\color{blue}{-11-11x } & = & 13 \color{red}{ +11x }\color{blue}{-11-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & 13 \color{blue}{-11} \\\Leftrightarrow &x & = &2\\\Leftrightarrow & \color{red}{}x & = &2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 2 \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{-7}& = & -12 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{-7}\color{blue}{+7-13x } & = & -12 \color{red}{ +13x }\color{blue}{+7-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & -12 \color{blue}{+7} \\\Leftrightarrow &-16x & = &-5\\\Leftrightarrow & \color{red}{-16}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-5}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{16} } & & \\ & V = \left\{ \frac{5}{16} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{+14}& = & 5 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+14}\color{blue}{-14+11x } & = & 5 \color{red}{ -11x }\color{blue}{-14+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 5 \color{blue}{-14} \\\Leftrightarrow &17x & = &-9\\\Leftrightarrow & \color{red}{17}x & = &-9\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-9}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{17} } & & \\ & V = \left\{ \frac{-9}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{-14}& = & -7 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-14}\color{blue}{+14-x } & = & -7 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -7 \color{blue}{+14} \\\Leftrightarrow &5x & = &7\\\Leftrightarrow & \color{red}{5}x & = &7\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{7}{5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{-12}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-12}\color{blue}{+12-x } & = & 7 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 7 \color{blue}{+12} \\\Leftrightarrow &5x & = &19\\\Leftrightarrow & \color{red}{5}x & = &19\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{19}{5} \\\Leftrightarrow & \color{green}{ x = \frac{19}{5} } & & \\ & V = \left\{ \frac{19}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{+2}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+2}\color{blue}{-2-x } & = & -7 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -7 \color{blue}{-2} \\\Leftrightarrow &-6x & = &-9\\\Leftrightarrow & \color{red}{-6}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-9}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{-14}& = & 12 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{-14}\color{blue}{+14-11x } & = & 12 \color{red}{ +11x }\color{blue}{+14-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & 12 \color{blue}{+14} \\\Leftrightarrow &-9x & = &26\\\Leftrightarrow & \color{red}{-9}x & = &26\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{26}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{9} } & & \\ & V = \left\{ \frac{-26}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{-15}& = & 3 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-15}\color{blue}{+15-7x } & = & 3 \color{red}{ +7x }\color{blue}{+15-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 3 \color{blue}{+15} \\\Leftrightarrow &3x & = &18\\\Leftrightarrow & \color{red}{3}x & = &18\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{18}{3} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{+6}& = & 11 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{+6}\color{blue}{-6+4x } & = & 11 \color{red}{ -4x }\color{blue}{-6+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & 11 \color{blue}{-6} \\\Leftrightarrow &9x & = &5\\\Leftrightarrow & \color{red}{9}x & = &5\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{5}{9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{9} } & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{+6}& = & 4 \color{red}{ -15x } \\\Leftrightarrow & -x \color{red}{+6}\color{blue}{-6+15x } & = & 4 \color{red}{ -15x }\color{blue}{-6+15x } \\\Leftrightarrow & -x \color{blue}{+15x } & = & 4 \color{blue}{-6} \\\Leftrightarrow &14x & = &-2\\\Leftrightarrow & \color{red}{14}x & = &-2\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-2}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{+8}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+8}\color{blue}{-8-x } & = & 2 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 2 \color{blue}{-8} \\\Leftrightarrow &-4x & = &-6\\\Leftrightarrow & \color{red}{-4}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-6}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{+6}& = & 7 \color{red}{ +13x } \\\Leftrightarrow & 14x \color{red}{+6}\color{blue}{-6-13x } & = & 7 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & 14x \color{blue}{-13x } & = & 7 \color{blue}{-6} \\\Leftrightarrow &x & = &1\\\Leftrightarrow & \color{red}{}x & = &1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 1 \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)