Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{+12}& = & 11 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{+12}\color{blue}{-12-10x } & = & 11 \color{red}{ +10x }\color{blue}{-12-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & 11 \color{blue}{-12} \\\Leftrightarrow &-19x & = &-1\\\Leftrightarrow & \color{red}{-19}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-1}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{1}{19} } & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{-11}& = & 8 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{-11}\color{blue}{+11+10x } & = & 8 \color{red}{ -10x }\color{blue}{+11+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & 8 \color{blue}{+11} \\\Leftrightarrow &21x & = &19\\\Leftrightarrow & \color{red}{21}x & = &19\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{19}{21} \\\Leftrightarrow & \color{green}{ x = \frac{19}{21} } & & \\ & V = \left\{ \frac{19}{21} \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{-10}& = & -8 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{-10}\color{blue}{+10-4x } & = & -8 \color{red}{ +4x }\color{blue}{+10-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & -8 \color{blue}{+10} \\\Leftrightarrow &-11x & = &2\\\Leftrightarrow & \color{red}{-11}x & = &2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{-8}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-8}\color{blue}{+8-x } & = & 11 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 11 \color{blue}{+8} \\\Leftrightarrow &-14x & = &19\\\Leftrightarrow & \color{red}{-14}x & = &19\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{19}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{14} } & & \\ & V = \left\{ \frac{-19}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{+9}& = & -3 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+9}\color{blue}{-9+11x } & = & -3 \color{red}{ -11x }\color{blue}{-9+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -3 \color{blue}{-9} \\\Leftrightarrow &23x & = &-12\\\Leftrightarrow & \color{red}{23}x & = &-12\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-12}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{23} } & & \\ & V = \left\{ \frac{-12}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{+6}& = & 6 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+6}\color{blue}{-6-13x } & = & 6 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 6 \color{blue}{-6} \\\Leftrightarrow &-19x & = &0\\\Leftrightarrow & \color{red}{-19}x & = &0\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{0}{-19} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{-10}& = & 14 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{-10}\color{blue}{+10-7x } & = & 14 \color{red}{ +7x }\color{blue}{+10-7x } \\\Leftrightarrow & -3x \color{blue}{-7x } & = & 14 \color{blue}{+10} \\\Leftrightarrow &-10x & = &24\\\Leftrightarrow & \color{red}{-10}x & = &24\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{24}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{5} } & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{+15}& = & -15 \color{red}{ -7x } \\\Leftrightarrow & 5x \color{red}{+15}\color{blue}{-15+7x } & = & -15 \color{red}{ -7x }\color{blue}{-15+7x } \\\Leftrightarrow & 5x \color{blue}{+7x } & = & -15 \color{blue}{-15} \\\Leftrightarrow &12x & = &-30\\\Leftrightarrow & \color{red}{12}x & = &-30\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-30}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{+3}& = & 1 \color{red}{ +5x } \\\Leftrightarrow & 14x \color{red}{+3}\color{blue}{-3-5x } & = & 1 \color{red}{ +5x }\color{blue}{-3-5x } \\\Leftrightarrow & 14x \color{blue}{-5x } & = & 1 \color{blue}{-3} \\\Leftrightarrow &9x & = &-2\\\Leftrightarrow & \color{red}{9}x & = &-2\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-2}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{-2}& = & 9 \color{red}{ +5x } \\\Leftrightarrow & 3x \color{red}{-2}\color{blue}{+2-5x } & = & 9 \color{red}{ +5x }\color{blue}{+2-5x } \\\Leftrightarrow & 3x \color{blue}{-5x } & = & 9 \color{blue}{+2} \\\Leftrightarrow &-2x & = &11\\\Leftrightarrow & \color{red}{-2}x & = &11\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{11}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{2} } & & \\ & V = \left\{ \frac{-11}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{-8}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-8}\color{blue}{+8-x } & = & -14 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -14 \color{blue}{+8} \\\Leftrightarrow &-14x & = &-6\\\Leftrightarrow & \color{red}{-14}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-6}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{+13}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+13}\color{blue}{-13-x } & = & -11 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -11 \color{blue}{-13} \\\Leftrightarrow &-10x & = &-24\\\Leftrightarrow & \color{red}{-10}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-24}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)