Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{-15}& = & 6 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{-15}\color{blue}{+15+11x } & = & 6 \color{red}{ -11x }\color{blue}{+15+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & 6 \color{blue}{+15} \\\Leftrightarrow &26x & = &21\\\Leftrightarrow & \color{red}{26}x & = &21\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{21}{26} \\\Leftrightarrow & \color{green}{ x = \frac{21}{26} } & & \\ & V = \left\{ \frac{21}{26} \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{-7}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -x \color{red}{-7}\color{blue}{+7-x } & = & -9 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -x \color{blue}{-x } & = & -9 \color{blue}{+7} \\\Leftrightarrow &-2x & = &-2\\\Leftrightarrow & \color{red}{-2}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-2}{-2} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{+10}& = & -9 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+10}\color{blue}{-10-5x } & = & -9 \color{red}{ +5x }\color{blue}{-10-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & -9 \color{blue}{-10} \\\Leftrightarrow &-14x & = &-19\\\Leftrightarrow & \color{red}{-14}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-19}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{19}{14} } & & \\ & V = \left\{ \frac{19}{14} \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{-8}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-8}\color{blue}{+8-x } & = & 7 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 7 \color{blue}{+8} \\\Leftrightarrow &-8x & = &15\\\Leftrightarrow & \color{red}{-8}x & = &15\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{15}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{8} } & & \\ & V = \left\{ \frac{-15}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{+14}& = & -12 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{+14}\color{blue}{-14-13x } & = & -12 \color{red}{ +13x }\color{blue}{-14-13x } \\\Leftrightarrow & 12x \color{blue}{-13x } & = & -12 \color{blue}{-14} \\\Leftrightarrow &-x & = &-26\\\Leftrightarrow & \color{red}{-}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-26}{-1} \\\Leftrightarrow & \color{green}{ x = 26 } & & \\ & V = \left\{ 26 \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{-11}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-11}\color{blue}{+11-x } & = & -1 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -1 \color{blue}{+11} \\\Leftrightarrow &-8x & = &10\\\Leftrightarrow & \color{red}{-8}x & = &10\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{10}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{+14}& = & -1 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{+14}\color{blue}{-14-7x } & = & -1 \color{red}{ +7x }\color{blue}{-14-7x } \\\Leftrightarrow & 12x \color{blue}{-7x } & = & -1 \color{blue}{-14} \\\Leftrightarrow &5x & = &-15\\\Leftrightarrow & \color{red}{5}x & = &-15\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-15}{5} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{-15}& = & -2 \color{red}{ +8x } \\\Leftrightarrow & -5x \color{red}{-15}\color{blue}{+15-8x } & = & -2 \color{red}{ +8x }\color{blue}{+15-8x } \\\Leftrightarrow & -5x \color{blue}{-8x } & = & -2 \color{blue}{+15} \\\Leftrightarrow &-13x & = &13\\\Leftrightarrow & \color{red}{-13}x & = &13\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{13}{-13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{+9}& = & 15 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+9}\color{blue}{-9+5x } & = & 15 \color{red}{ -5x }\color{blue}{-9+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 15 \color{blue}{-9} \\\Leftrightarrow &11x & = &6\\\Leftrightarrow & \color{red}{11}x & = &6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{6}{11} } & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{+15}& = & -9 \color{red}{ +12x } \\\Leftrightarrow & 13x \color{red}{+15}\color{blue}{-15-12x } & = & -9 \color{red}{ +12x }\color{blue}{-15-12x } \\\Leftrightarrow & 13x \color{blue}{-12x } & = & -9 \color{blue}{-15} \\\Leftrightarrow &x & = &-24\\\Leftrightarrow & \color{red}{}x & = &-24\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -24 \\\Leftrightarrow & \color{green}{ x = -24 } & & \\ & V = \left\{ -24 \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{+13}& = & -2 \color{red}{ +11x } \\\Leftrightarrow & -2x \color{red}{+13}\color{blue}{-13-11x } & = & -2 \color{red}{ +11x }\color{blue}{-13-11x } \\\Leftrightarrow & -2x \color{blue}{-11x } & = & -2 \color{blue}{-13} \\\Leftrightarrow &-13x & = &-15\\\Leftrightarrow & \color{red}{-13}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-15}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{15}{13} } & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{-2}& = & 3 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{-2}\color{blue}{+2+8x } & = & 3 \color{red}{ -8x }\color{blue}{+2+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & 3 \color{blue}{+2} \\\Leftrightarrow &17x & = &5\\\Leftrightarrow & \color{red}{17}x & = &5\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{5}{17} \\\Leftrightarrow & \color{green}{ x = \frac{5}{17} } & & \\ & V = \left\{ \frac{5}{17} \right\} & \\\end{align}\)