Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{+2}& = & 13 \color{red}{ +6x } \\\Leftrightarrow & x \color{red}{+2}\color{blue}{-2-6x } & = & 13 \color{red}{ +6x }\color{blue}{-2-6x } \\\Leftrightarrow & x \color{blue}{-6x } & = & 13 \color{blue}{-2} \\\Leftrightarrow &-5x & = &11\\\Leftrightarrow & \color{red}{-5}x & = &11\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{11}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{5} } & & \\ & V = \left\{ \frac{-11}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{+13}& = & 1 \color{red}{ +13x } \\\Leftrightarrow & -2x \color{red}{+13}\color{blue}{-13-13x } & = & 1 \color{red}{ +13x }\color{blue}{-13-13x } \\\Leftrightarrow & -2x \color{blue}{-13x } & = & 1 \color{blue}{-13} \\\Leftrightarrow &-15x & = &-12\\\Leftrightarrow & \color{red}{-15}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{-1}& = & -1 \color{red}{ -2x } \\\Leftrightarrow & 7x \color{red}{-1}\color{blue}{+1+2x } & = & -1 \color{red}{ -2x }\color{blue}{+1+2x } \\\Leftrightarrow & 7x \color{blue}{+2x } & = & -1 \color{blue}{+1} \\\Leftrightarrow &9x & = &0\\\Leftrightarrow & \color{red}{9}x & = &0\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{0}{9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{+3}& = & -9 \color{red}{ +11x } \\\Leftrightarrow & 10x \color{red}{+3}\color{blue}{-3-11x } & = & -9 \color{red}{ +11x }\color{blue}{-3-11x } \\\Leftrightarrow & 10x \color{blue}{-11x } & = & -9 \color{blue}{-3} \\\Leftrightarrow &-x & = &-12\\\Leftrightarrow & \color{red}{-}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-12}{-1} \\\Leftrightarrow & \color{green}{ x = 12 } & & \\ & V = \left\{ 12 \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{-5}& = & 6 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-5}\color{blue}{+5-9x } & = & 6 \color{red}{ +9x }\color{blue}{+5-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & 6 \color{blue}{+5} \\\Leftrightarrow &-13x & = &11\\\Leftrightarrow & \color{red}{-13}x & = &11\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{11}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{13} } & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{+12}& = & 11 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+12}\color{blue}{-12+13x } & = & 11 \color{red}{ -13x }\color{blue}{-12+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 11 \color{blue}{-12} \\\Leftrightarrow &27x & = &-1\\\Leftrightarrow & \color{red}{27}x & = &-1\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-1}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{27} } & & \\ & V = \left\{ \frac{-1}{27} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{-15}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-15}\color{blue}{+15-x } & = & 15 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 15 \color{blue}{+15} \\\Leftrightarrow &-12x & = &30\\\Leftrightarrow & \color{red}{-12}x & = &30\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{30}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{+7}& = & 9 \color{red}{ +9x } \\\Leftrightarrow & 2x \color{red}{+7}\color{blue}{-7-9x } & = & 9 \color{red}{ +9x }\color{blue}{-7-9x } \\\Leftrightarrow & 2x \color{blue}{-9x } & = & 9 \color{blue}{-7} \\\Leftrightarrow &-7x & = &2\\\Leftrightarrow & \color{red}{-7}x & = &2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{+14}& = & 13 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+14}\color{blue}{-14+2x } & = & 13 \color{red}{ -2x }\color{blue}{-14+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 13 \color{blue}{-14} \\\Leftrightarrow &17x & = &-1\\\Leftrightarrow & \color{red}{17}x & = &-1\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-1}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{17} } & & \\ & V = \left\{ \frac{-1}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{+5}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{+5}\color{blue}{-5-13x } & = & 11 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & 11 \color{blue}{-5} \\\Leftrightarrow &-16x & = &6\\\Leftrightarrow & \color{red}{-16}x & = &6\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{6}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{-8}& = & 8 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{-8}\color{blue}{+8+13x } & = & 8 \color{red}{ -13x }\color{blue}{+8+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & 8 \color{blue}{+8} \\\Leftrightarrow &20x & = &16\\\Leftrightarrow & \color{red}{20}x & = &16\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{16}{20} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{+9}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{+9}\color{blue}{-9-x } & = & -1 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & -1 \color{blue}{-9} \\\Leftrightarrow &4x & = &-10\\\Leftrightarrow & \color{red}{4}x & = &-10\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-10}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)