Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{+11}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & 11x \color{red}{+11}\color{blue}{-11-13x } & = & 13 \color{red}{ +13x }\color{blue}{-11-13x } \\\Leftrightarrow & 11x \color{blue}{-13x } & = & 13 \color{blue}{-11} \\\Leftrightarrow &-2x & = &2\\\Leftrightarrow & \color{red}{-2}x & = &2\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{2}{-2} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{-10}& = & 1 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-10}\color{blue}{+10+13x } & = & 1 \color{red}{ -13x }\color{blue}{+10+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & 1 \color{blue}{+10} \\\Leftrightarrow &23x & = &11\\\Leftrightarrow & \color{red}{23}x & = &11\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{11}{23} \\\Leftrightarrow & \color{green}{ x = \frac{11}{23} } & & \\ & V = \left\{ \frac{11}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{+9}& = & 10 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+9}\color{blue}{-9+13x } & = & 10 \color{red}{ -13x }\color{blue}{-9+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & 10 \color{blue}{-9} \\\Leftrightarrow &23x & = &1\\\Leftrightarrow & \color{red}{23}x & = &1\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{1}{23} \\\Leftrightarrow & \color{green}{ x = \frac{1}{23} } & & \\ & V = \left\{ \frac{1}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{+2}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+2}\color{blue}{-2-x } & = & -12 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -12 \color{blue}{-2} \\\Leftrightarrow &-12x & = &-14\\\Leftrightarrow & \color{red}{-12}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-14}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{6} } & & \\ & V = \left\{ \frac{7}{6} \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{-4}& = & 12 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-4}\color{blue}{+4-9x } & = & 12 \color{red}{ +9x }\color{blue}{+4-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & 12 \color{blue}{+4} \\\Leftrightarrow &-13x & = &16\\\Leftrightarrow & \color{red}{-13}x & = &16\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{16}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{13} } & & \\ & V = \left\{ \frac{-16}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{+13}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+13}\color{blue}{-13-x } & = & 10 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 10 \color{blue}{-13} \\\Leftrightarrow &-11x & = &-3\\\Leftrightarrow & \color{red}{-11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{+14}& = & -11 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+14}\color{blue}{-14+3x } & = & -11 \color{red}{ -3x }\color{blue}{-14+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -11 \color{blue}{-14} \\\Leftrightarrow &13x & = &-25\\\Leftrightarrow & \color{red}{13}x & = &-25\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-25}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{13} } & & \\ & V = \left\{ \frac{-25}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{-4}& = & 8 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-4}\color{blue}{+4+13x } & = & 8 \color{red}{ -13x }\color{blue}{+4+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 8 \color{blue}{+4} \\\Leftrightarrow &27x & = &12\\\Leftrightarrow & \color{red}{27}x & = &12\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{12}{27} \\\Leftrightarrow & \color{green}{ x = \frac{4}{9} } & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{+7}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+7}\color{blue}{-7-13x } & = & 13 \color{red}{ +13x }\color{blue}{-7-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 13 \color{blue}{-7} \\\Leftrightarrow &-19x & = &6\\\Leftrightarrow & \color{red}{-19}x & = &6\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{6}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{19} } & & \\ & V = \left\{ \frac{-6}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{+4}& = & -14 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{+4}\color{blue}{-4+15x } & = & -14 \color{red}{ -15x }\color{blue}{-4+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & -14 \color{blue}{-4} \\\Leftrightarrow &23x & = &-18\\\Leftrightarrow & \color{red}{23}x & = &-18\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-18}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{23} } & & \\ & V = \left\{ \frac{-18}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{+6}& = & 12 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+6}\color{blue}{-6-7x } & = & 12 \color{red}{ +7x }\color{blue}{-6-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 12 \color{blue}{-6} \\\Leftrightarrow &3x & = &6\\\Leftrightarrow & \color{red}{3}x & = &6\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{6}{3} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{+13}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+13}\color{blue}{-13-x } & = & 12 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 12 \color{blue}{-13} \\\Leftrightarrow &-15x & = &-1\\\Leftrightarrow & \color{red}{-15}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{15} } & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)