Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{-4}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-4}\color{blue}{+4-x } & = & -9 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -9 \color{blue}{+4} \\\Leftrightarrow &-13x & = &-5\\\Leftrightarrow & \color{red}{-13}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-5}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{5}{13} } & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{+4}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+4}\color{blue}{-4-x } & = & -8 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -8 \color{blue}{-4} \\\Leftrightarrow &-3x & = &-12\\\Leftrightarrow & \color{red}{-3}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-12}{-3} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{-11}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-11}\color{blue}{+11-x } & = & 2 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 2 \color{blue}{+11} \\\Leftrightarrow &-11x & = &13\\\Leftrightarrow & \color{red}{-11}x & = &13\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{13}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{11} } & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{+10}& = & -9 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+10}\color{blue}{-10+11x } & = & -9 \color{red}{ -11x }\color{blue}{-10+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -9 \color{blue}{-10} \\\Leftrightarrow &17x & = &-19\\\Leftrightarrow & \color{red}{17}x & = &-19\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-19}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{17} } & & \\ & V = \left\{ \frac{-19}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{+11}& = & 1 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+11}\color{blue}{-11+13x } & = & 1 \color{red}{ -13x }\color{blue}{-11+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 1 \color{blue}{-11} \\\Leftrightarrow &27x & = &-10\\\Leftrightarrow & \color{red}{27}x & = &-10\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-10}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{27} } & & \\ & V = \left\{ \frac{-10}{27} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{-15}& = & 14 \color{red}{ -2x } \\\Leftrightarrow & 5x \color{red}{-15}\color{blue}{+15+2x } & = & 14 \color{red}{ -2x }\color{blue}{+15+2x } \\\Leftrightarrow & 5x \color{blue}{+2x } & = & 14 \color{blue}{+15} \\\Leftrightarrow &7x & = &29\\\Leftrightarrow & \color{red}{7}x & = &29\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{29}{7} \\\Leftrightarrow & \color{green}{ x = \frac{29}{7} } & & \\ & V = \left\{ \frac{29}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{+9}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & 9x \color{red}{+9}\color{blue}{-9-13x } & = & 11 \color{red}{ +13x }\color{blue}{-9-13x } \\\Leftrightarrow & 9x \color{blue}{-13x } & = & 11 \color{blue}{-9} \\\Leftrightarrow &-4x & = &2\\\Leftrightarrow & \color{red}{-4}x & = &2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{-12}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-12}\color{blue}{+12-x } & = & 5 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 5 \color{blue}{+12} \\\Leftrightarrow &-6x & = &17\\\Leftrightarrow & \color{red}{-6}x & = &17\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{17}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{6} } & & \\ & V = \left\{ \frac{-17}{6} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{-8}& = & -4 \color{red}{ +4x } \\\Leftrightarrow & 7x \color{red}{-8}\color{blue}{+8-4x } & = & -4 \color{red}{ +4x }\color{blue}{+8-4x } \\\Leftrightarrow & 7x \color{blue}{-4x } & = & -4 \color{blue}{+8} \\\Leftrightarrow &3x & = &4\\\Leftrightarrow & \color{red}{3}x & = &4\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{4}{3} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{+12}& = & 8 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{+12}\color{blue}{-12+10x } & = & 8 \color{red}{ -10x }\color{blue}{-12+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & 8 \color{blue}{-12} \\\Leftrightarrow &21x & = &-4\\\Leftrightarrow & \color{red}{21}x & = &-4\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-4}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{21} } & & \\ & V = \left\{ \frac{-4}{21} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{+6}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+6}\color{blue}{-6-x } & = & 2 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 2 \color{blue}{-6} \\\Leftrightarrow &-5x & = &-4\\\Leftrightarrow & \color{red}{-5}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-4}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{-9}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-9}\color{blue}{+9-x } & = & -13 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -13 \color{blue}{+9} \\\Leftrightarrow &-5x & = &-4\\\Leftrightarrow & \color{red}{-5}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-4}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)