Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{+7}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{+7}\color{blue}{-7-x } & = & -11 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & -11 \color{blue}{-7} \\\Leftrightarrow &4x & = &-18\\\Leftrightarrow & \color{red}{4}x & = &-18\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-18}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{2} } & & \\ & V = \left\{ \frac{-9}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{-3}& = & -12 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{-3}\color{blue}{+3-12x } & = & -12 \color{red}{ +12x }\color{blue}{+3-12x } \\\Leftrightarrow & 11x \color{blue}{-12x } & = & -12 \color{blue}{+3} \\\Leftrightarrow &-x & = &-9\\\Leftrightarrow & \color{red}{-}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-9}{-1} \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{+14}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+14}\color{blue}{-14-x } & = & 10 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 10 \color{blue}{-14} \\\Leftrightarrow &-9x & = &-4\\\Leftrightarrow & \color{red}{-9}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-4}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{9} } & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & x \color{red}{+3}& = & 7 \color{red}{ -4x } \\\Leftrightarrow & x \color{red}{+3}\color{blue}{-3+4x } & = & 7 \color{red}{ -4x }\color{blue}{-3+4x } \\\Leftrightarrow & x \color{blue}{+4x } & = & 7 \color{blue}{-3} \\\Leftrightarrow &5x & = &4\\\Leftrightarrow & \color{red}{5}x & = &4\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{4}{5} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{-3}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-3}\color{blue}{+3-x } & = & 3 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 3 \color{blue}{+3} \\\Leftrightarrow &-14x & = &6\\\Leftrightarrow & \color{red}{-14}x & = &6\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{6}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{+14}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+14}\color{blue}{-14-x } & = & 4 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 4 \color{blue}{-14} \\\Leftrightarrow &-4x & = &-10\\\Leftrightarrow & \color{red}{-4}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-10}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{-8}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-8}\color{blue}{+8-x } & = & -3 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -3 \color{blue}{+8} \\\Leftrightarrow &-11x & = &5\\\Leftrightarrow & \color{red}{-11}x & = &5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{-10}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{-10}\color{blue}{+10-x } & = & 3 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & 3 \color{blue}{+10} \\\Leftrightarrow &6x & = &13\\\Leftrightarrow & \color{red}{6}x & = &13\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{13}{6} \\\Leftrightarrow & \color{green}{ x = \frac{13}{6} } & & \\ & V = \left\{ \frac{13}{6} \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{+1}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{+1}\color{blue}{-1-13x } & = & 13 \color{red}{ +13x }\color{blue}{-1-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & 13 \color{blue}{-1} \\\Leftrightarrow &-16x & = &12\\\Leftrightarrow & \color{red}{-16}x & = &12\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{12}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{-3}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-3}\color{blue}{+3-x } & = & 8 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 8 \color{blue}{+3} \\\Leftrightarrow &-10x & = &11\\\Leftrightarrow & \color{red}{-10}x & = &11\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{11}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{10} } & & \\ & V = \left\{ \frac{-11}{10} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{+2}& = & 15 \color{red}{ -11x } \\\Leftrightarrow & -x \color{red}{+2}\color{blue}{-2+11x } & = & 15 \color{red}{ -11x }\color{blue}{-2+11x } \\\Leftrightarrow & -x \color{blue}{+11x } & = & 15 \color{blue}{-2} \\\Leftrightarrow &10x & = &13\\\Leftrightarrow & \color{red}{10}x & = &13\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{13}{10} \\\Leftrightarrow & \color{green}{ x = \frac{13}{10} } & & \\ & V = \left\{ \frac{13}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{-13}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-13}\color{blue}{+13-x } & = & 7 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 7 \color{blue}{+13} \\\Leftrightarrow &11x & = &20\\\Leftrightarrow & \color{red}{11}x & = &20\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{20}{11} \\\Leftrightarrow & \color{green}{ x = \frac{20}{11} } & & \\ & V = \left\{ \frac{20}{11} \right\} & \\\end{align}\)