Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{-7}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-7}\color{blue}{+7-x } & = & 12 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 12 \color{blue}{+7} \\\Leftrightarrow &-6x & = &19\\\Leftrightarrow & \color{red}{-6}x & = &19\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{19}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{6} } & & \\ & V = \left\{ \frac{-19}{6} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{-12}& = & 12 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{-12}\color{blue}{+12+5x } & = & 12 \color{red}{ -5x }\color{blue}{+12+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 12 \color{blue}{+12} \\\Leftrightarrow &11x & = &24\\\Leftrightarrow & \color{red}{11}x & = &24\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{24}{11} \\\Leftrightarrow & \color{green}{ x = \frac{24}{11} } & & \\ & V = \left\{ \frac{24}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{-2}& = & 3 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{-2}\color{blue}{+2+13x } & = & 3 \color{red}{ -13x }\color{blue}{+2+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & 3 \color{blue}{+2} \\\Leftrightarrow &22x & = &5\\\Leftrightarrow & \color{red}{22}x & = &5\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{5}{22} \\\Leftrightarrow & \color{green}{ x = \frac{5}{22} } & & \\ & V = \left\{ \frac{5}{22} \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{-14}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-14}\color{blue}{+14-x } & = & -8 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -8 \color{blue}{+14} \\\Leftrightarrow &-10x & = &6\\\Leftrightarrow & \color{red}{-10}x & = &6\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{6}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{-15}& = & -5 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-15}\color{blue}{+15+13x } & = & -5 \color{red}{ -13x }\color{blue}{+15+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -5 \color{blue}{+15} \\\Leftrightarrow &27x & = &10\\\Leftrightarrow & \color{red}{27}x & = &10\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{10}{27} \\\Leftrightarrow & \color{green}{ x = \frac{10}{27} } & & \\ & V = \left\{ \frac{10}{27} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{-9}& = & 4 \color{red}{ +13x } \\\Leftrightarrow & 7x \color{red}{-9}\color{blue}{+9-13x } & = & 4 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & 7x \color{blue}{-13x } & = & 4 \color{blue}{+9} \\\Leftrightarrow &-6x & = &13\\\Leftrightarrow & \color{red}{-6}x & = &13\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{13}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{6} } & & \\ & V = \left\{ \frac{-13}{6} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{-7}& = & 15 \color{red}{ +13x } \\\Leftrightarrow & 2x \color{red}{-7}\color{blue}{+7-13x } & = & 15 \color{red}{ +13x }\color{blue}{+7-13x } \\\Leftrightarrow & 2x \color{blue}{-13x } & = & 15 \color{blue}{+7} \\\Leftrightarrow &-11x & = &22\\\Leftrightarrow & \color{red}{-11}x & = &22\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{22}{-11} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{+11}& = & 7 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+11}\color{blue}{-11+11x } & = & 7 \color{red}{ -11x }\color{blue}{-11+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 7 \color{blue}{-11} \\\Leftrightarrow &17x & = &-4\\\Leftrightarrow & \color{red}{17}x & = &-4\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-4}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{17} } & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{+7}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+7}\color{blue}{-7-x } & = & -12 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -12 \color{blue}{-7} \\\Leftrightarrow &11x & = &-19\\\Leftrightarrow & \color{red}{11}x & = &-19\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-19}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{11} } & & \\ & V = \left\{ \frac{-19}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{-2}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-2}\color{blue}{+2-x } & = & -13 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -13 \color{blue}{+2} \\\Leftrightarrow &-11x & = &-11\\\Leftrightarrow & \color{red}{-11}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-11}{-11} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{+14}& = & 5 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+14}\color{blue}{-14-x } & = & 5 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 5 \color{blue}{-14} \\\Leftrightarrow &5x & = &-9\\\Leftrightarrow & \color{red}{5}x & = &-9\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-9}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{-9}& = & -9 \color{red}{ +9x } \\\Leftrightarrow & 2x \color{red}{-9}\color{blue}{+9-9x } & = & -9 \color{red}{ +9x }\color{blue}{+9-9x } \\\Leftrightarrow & 2x \color{blue}{-9x } & = & -9 \color{blue}{+9} \\\Leftrightarrow &-7x & = &0\\\Leftrightarrow & \color{red}{-7}x & = &0\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{0}{-7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)