Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{+8}& = & 12 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{+8}\color{blue}{-8-9x } & = & 12 \color{red}{ +9x }\color{blue}{-8-9x } \\\Leftrightarrow & 4x \color{blue}{-9x } & = & 12 \color{blue}{-8} \\\Leftrightarrow &-5x & = &4\\\Leftrightarrow & \color{red}{-5}x & = &4\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{4}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{+2}& = & 12 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+2}\color{blue}{-2+13x } & = & 12 \color{red}{ -13x }\color{blue}{-2+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & 12 \color{blue}{-2} \\\Leftrightarrow &23x & = &10\\\Leftrightarrow & \color{red}{23}x & = &10\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{10}{23} \\\Leftrightarrow & \color{green}{ x = \frac{10}{23} } & & \\ & V = \left\{ \frac{10}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{+7}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+7}\color{blue}{-7-x } & = & -5 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -5 \color{blue}{-7} \\\Leftrightarrow &-7x & = &-12\\\Leftrightarrow & \color{red}{-7}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-12}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{12}{7} } & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{-12}& = & 6 \color{red}{ -5x } \\\Leftrightarrow & 8x \color{red}{-12}\color{blue}{+12+5x } & = & 6 \color{red}{ -5x }\color{blue}{+12+5x } \\\Leftrightarrow & 8x \color{blue}{+5x } & = & 6 \color{blue}{+12} \\\Leftrightarrow &13x & = &18\\\Leftrightarrow & \color{red}{13}x & = &18\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{18}{13} \\\Leftrightarrow & \color{green}{ x = \frac{18}{13} } & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{-8}& = & 3 \color{red}{ +11x } \\\Leftrightarrow & 10x \color{red}{-8}\color{blue}{+8-11x } & = & 3 \color{red}{ +11x }\color{blue}{+8-11x } \\\Leftrightarrow & 10x \color{blue}{-11x } & = & 3 \color{blue}{+8} \\\Leftrightarrow &-x & = &11\\\Leftrightarrow & \color{red}{-}x & = &11\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{11}{-1} \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{+5}& = & 6 \color{red}{ +9x } \\\Leftrightarrow & 13x \color{red}{+5}\color{blue}{-5-9x } & = & 6 \color{red}{ +9x }\color{blue}{-5-9x } \\\Leftrightarrow & 13x \color{blue}{-9x } & = & 6 \color{blue}{-5} \\\Leftrightarrow &4x & = &1\\\Leftrightarrow & \color{red}{4}x & = &1\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{1}{4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{-6}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-6}\color{blue}{+6-x } & = & 11 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 11 \color{blue}{+6} \\\Leftrightarrow &-10x & = &17\\\Leftrightarrow & \color{red}{-10}x & = &17\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{17}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{10} } & & \\ & V = \left\{ \frac{-17}{10} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{-13}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-13}\color{blue}{+13-x } & = & 7 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 7 \color{blue}{+13} \\\Leftrightarrow &-8x & = &20\\\Leftrightarrow & \color{red}{-8}x & = &20\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{20}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{-2}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-2}\color{blue}{+2-13x } & = & 11 \color{red}{ +13x }\color{blue}{+2-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 11 \color{blue}{+2} \\\Leftrightarrow &-25x & = &13\\\Leftrightarrow & \color{red}{-25}x & = &13\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{13}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{25} } & & \\ & V = \left\{ \frac{-13}{25} \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{+14}& = & 4 \color{red}{ +9x } \\\Leftrightarrow & -2x \color{red}{+14}\color{blue}{-14-9x } & = & 4 \color{red}{ +9x }\color{blue}{-14-9x } \\\Leftrightarrow & -2x \color{blue}{-9x } & = & 4 \color{blue}{-14} \\\Leftrightarrow &-11x & = &-10\\\Leftrightarrow & \color{red}{-11}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-10}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{10}{11} } & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{+2}& = & 6 \color{red}{ +3x } \\\Leftrightarrow & 7x \color{red}{+2}\color{blue}{-2-3x } & = & 6 \color{red}{ +3x }\color{blue}{-2-3x } \\\Leftrightarrow & 7x \color{blue}{-3x } & = & 6 \color{blue}{-2} \\\Leftrightarrow &4x & = &4\\\Leftrightarrow & \color{red}{4}x & = &4\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{4}{4} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{-12}& = & 12 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-12}\color{blue}{+12-13x } & = & 12 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 12 \color{blue}{+12} \\\Leftrightarrow &-19x & = &24\\\Leftrightarrow & \color{red}{-19}x & = &24\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{24}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{19} } & & \\ & V = \left\{ \frac{-24}{19} \right\} & \\\end{align}\)