Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{-9}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-9}\color{blue}{+9-x } & = & 4 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 4 \color{blue}{+9} \\\Leftrightarrow &-13x & = &13\\\Leftrightarrow & \color{red}{-13}x & = &13\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{13}{-13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{-4}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-4}\color{blue}{+4-x } & = & -15 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -15 \color{blue}{+4} \\\Leftrightarrow &-9x & = &-11\\\Leftrightarrow & \color{red}{-9}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-11}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{11}{9} } & & \\ & V = \left\{ \frac{11}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{-13}& = & 8 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{-13}\color{blue}{+13+11x } & = & 8 \color{red}{ -11x }\color{blue}{+13+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & 8 \color{blue}{+13} \\\Leftrightarrow &26x & = &21\\\Leftrightarrow & \color{red}{26}x & = &21\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{21}{26} \\\Leftrightarrow & \color{green}{ x = \frac{21}{26} } & & \\ & V = \left\{ \frac{21}{26} \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{-5}& = & 3 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-5}\color{blue}{+5+13x } & = & 3 \color{red}{ -13x }\color{blue}{+5+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 3 \color{blue}{+5} \\\Leftrightarrow &27x & = &8\\\Leftrightarrow & \color{red}{27}x & = &8\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{8}{27} \\\Leftrightarrow & \color{green}{ x = \frac{8}{27} } & & \\ & V = \left\{ \frac{8}{27} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{-11}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-11}\color{blue}{+11-x } & = & 9 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 9 \color{blue}{+11} \\\Leftrightarrow &-9x & = &20\\\Leftrightarrow & \color{red}{-9}x & = &20\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{20}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{9} } & & \\ & V = \left\{ \frac{-20}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{+10}& = & 6 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+10}\color{blue}{-10-7x } & = & 6 \color{red}{ +7x }\color{blue}{-10-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 6 \color{blue}{-10} \\\Leftrightarrow &-17x & = &-4\\\Leftrightarrow & \color{red}{-17}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-4}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{4}{17} } & & \\ & V = \left\{ \frac{4}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{-4}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-4}\color{blue}{+4-x } & = & -8 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -8 \color{blue}{+4} \\\Leftrightarrow &-5x & = &-4\\\Leftrightarrow & \color{red}{-5}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-4}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{+13}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{+13}\color{blue}{-13-x } & = & 9 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & 9 \color{blue}{-13} \\\Leftrightarrow &6x & = &-4\\\Leftrightarrow & \color{red}{6}x & = &-4\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-4}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{+9}& = & 10 \color{red}{ +12x } \\\Leftrightarrow & x \color{red}{+9}\color{blue}{-9-12x } & = & 10 \color{red}{ +12x }\color{blue}{-9-12x } \\\Leftrightarrow & x \color{blue}{-12x } & = & 10 \color{blue}{-9} \\\Leftrightarrow &-11x & = &1\\\Leftrightarrow & \color{red}{-11}x & = &1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{+15}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{+15}\color{blue}{-15-x } & = & -14 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & -14 \color{blue}{-15} \\\Leftrightarrow &8x & = &-29\\\Leftrightarrow & \color{red}{8}x & = &-29\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-29}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{8} } & & \\ & V = \left\{ \frac{-29}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{+10}& = & -1 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{+10}\color{blue}{-10-6x } & = & -1 \color{red}{ +6x }\color{blue}{-10-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & -1 \color{blue}{-10} \\\Leftrightarrow &-11x & = &-11\\\Leftrightarrow & \color{red}{-11}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-11}{-11} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{+7}& = & -11 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+7}\color{blue}{-7-13x } & = & -11 \color{red}{ +13x }\color{blue}{-7-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -11 \color{blue}{-7} \\\Leftrightarrow &-28x & = &-18\\\Leftrightarrow & \color{red}{-28}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-18}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{9}{14} } & & \\ & V = \left\{ \frac{9}{14} \right\} & \\\end{align}\)