Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{+1}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+1}\color{blue}{-1-x } & = & -4 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -4 \color{blue}{-1} \\\Leftrightarrow &-11x & = &-5\\\Leftrightarrow & \color{red}{-11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{-5}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-5}\color{blue}{+5-x } & = & 7 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 7 \color{blue}{+5} \\\Leftrightarrow &-10x & = &12\\\Leftrightarrow & \color{red}{-10}x & = &12\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{12}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{+14}& = & -13 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{+14}\color{blue}{-14+11x } & = & -13 \color{red}{ -11x }\color{blue}{-14+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & -13 \color{blue}{-14} \\\Leftrightarrow &26x & = &-27\\\Leftrightarrow & \color{red}{26}x & = &-27\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{-27}{26} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{26} } & & \\ & V = \left\{ \frac{-27}{26} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{+11}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+11}\color{blue}{-11-x } & = & -4 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -4 \color{blue}{-11} \\\Leftrightarrow &-7x & = &-15\\\Leftrightarrow & \color{red}{-7}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-15}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{15}{7} } & & \\ & V = \left\{ \frac{15}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{-10}& = & 9 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{-10}\color{blue}{+10-11x } & = & 9 \color{red}{ +11x }\color{blue}{+10-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & 9 \color{blue}{+10} \\\Leftrightarrow &-9x & = &19\\\Leftrightarrow & \color{red}{-9}x & = &19\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{19}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{9} } & & \\ & V = \left\{ \frac{-19}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{+11}& = & 10 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{+11}\color{blue}{-11+10x } & = & 10 \color{red}{ -10x }\color{blue}{-11+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & 10 \color{blue}{-11} \\\Leftrightarrow &21x & = &-1\\\Leftrightarrow & \color{red}{21}x & = &-1\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-1}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{21} } & & \\ & V = \left\{ \frac{-1}{21} \right\} & \\\end{align}\)
7. \(\begin{align} & 6x \color{red}{-9}& = & 4 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-9}\color{blue}{+9+11x } & = & 4 \color{red}{ -11x }\color{blue}{+9+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 4 \color{blue}{+9} \\\Leftrightarrow &17x & = &13\\\Leftrightarrow & \color{red}{17}x & = &13\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{13}{17} \\\Leftrightarrow & \color{green}{ x = \frac{13}{17} } & & \\ & V = \left\{ \frac{13}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{-3}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-3}\color{blue}{+3-x } & = & 10 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 10 \color{blue}{+3} \\\Leftrightarrow &-10x & = &13\\\Leftrightarrow & \color{red}{-10}x & = &13\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{13}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{10} } & & \\ & V = \left\{ \frac{-13}{10} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{-3}& = & 14 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{-3}\color{blue}{+3+13x } & = & 14 \color{red}{ -13x }\color{blue}{+3+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & 14 \color{blue}{+3} \\\Leftrightarrow &20x & = &17\\\Leftrightarrow & \color{red}{20}x & = &17\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{17}{20} \\\Leftrightarrow & \color{green}{ x = \frac{17}{20} } & & \\ & V = \left\{ \frac{17}{20} \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{-11}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{-11}\color{blue}{+11-7x } & = & -3 \color{red}{ +7x }\color{blue}{+11-7x } \\\Leftrightarrow & -3x \color{blue}{-7x } & = & -3 \color{blue}{+11} \\\Leftrightarrow &-10x & = &8\\\Leftrightarrow & \color{red}{-10}x & = &8\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{8}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{+2}& = & -11 \color{red}{ +6x } \\\Leftrightarrow & x \color{red}{+2}\color{blue}{-2-6x } & = & -11 \color{red}{ +6x }\color{blue}{-2-6x } \\\Leftrightarrow & x \color{blue}{-6x } & = & -11 \color{blue}{-2} \\\Leftrightarrow &-5x & = &-13\\\Leftrightarrow & \color{red}{-5}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-13}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{13}{5} } & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{+13}& = & -6 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+13}\color{blue}{-13-13x } & = & -6 \color{red}{ +13x }\color{blue}{-13-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -6 \color{blue}{-13} \\\Leftrightarrow &-25x & = &-19\\\Leftrightarrow & \color{red}{-25}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-19}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{19}{25} } & & \\ & V = \left\{ \frac{19}{25} \right\} & \\\end{align}\)