Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{-3}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-3}\color{blue}{+3-x } & = & 15 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 15 \color{blue}{+3} \\\Leftrightarrow &-7x & = &18\\\Leftrightarrow & \color{red}{-7}x & = &18\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{18}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{7} } & & \\ & V = \left\{ \frac{-18}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{+12}& = & 10 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{+12}\color{blue}{-12+2x } & = & 10 \color{red}{ -2x }\color{blue}{-12+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & 10 \color{blue}{-12} \\\Leftrightarrow &13x & = &-2\\\Leftrightarrow & \color{red}{13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-2}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{13} } & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{-15}& = & 14 \color{red}{ +11x } \\\Leftrightarrow & -13x \color{red}{-15}\color{blue}{+15-11x } & = & 14 \color{red}{ +11x }\color{blue}{+15-11x } \\\Leftrightarrow & -13x \color{blue}{-11x } & = & 14 \color{blue}{+15} \\\Leftrightarrow &-24x & = &29\\\Leftrightarrow & \color{red}{-24}x & = &29\\\Leftrightarrow & \frac{\color{red}{-24}x}{ \color{blue}{ -24}} & = & \frac{29}{-24} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{24} } & & \\ & V = \left\{ \frac{-29}{24} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{+13}& = & -8 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+13}\color{blue}{-13-13x } & = & -8 \color{red}{ +13x }\color{blue}{-13-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -8 \color{blue}{-13} \\\Leftrightarrow &-19x & = &-21\\\Leftrightarrow & \color{red}{-19}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-21}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{21}{19} } & & \\ & V = \left\{ \frac{21}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{-14}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-14}\color{blue}{+14-x } & = & 12 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 12 \color{blue}{+14} \\\Leftrightarrow &-15x & = &26\\\Leftrightarrow & \color{red}{-15}x & = &26\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{26}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{15} } & & \\ & V = \left\{ \frac{-26}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{+14}& = & -11 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{+14}\color{blue}{-14-11x } & = & -11 \color{red}{ +11x }\color{blue}{-14-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & -11 \color{blue}{-14} \\\Leftrightarrow &-9x & = &-25\\\Leftrightarrow & \color{red}{-9}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-25}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{25}{9} } & & \\ & V = \left\{ \frac{25}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{+7}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+7}\color{blue}{-7-x } & = & 6 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 6 \color{blue}{-7} \\\Leftrightarrow &-12x & = &-1\\\Leftrightarrow & \color{red}{-12}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-1}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{12} } & & \\ & V = \left\{ \frac{1}{12} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{+7}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+7}\color{blue}{-7-x } & = & -1 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -1 \color{blue}{-7} \\\Leftrightarrow &-15x & = &-8\\\Leftrightarrow & \color{red}{-15}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{8}{15} } & & \\ & V = \left\{ \frac{8}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{+7}& = & 4 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+7}\color{blue}{-7-13x } & = & 4 \color{red}{ +13x }\color{blue}{-7-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 4 \color{blue}{-7} \\\Leftrightarrow &-19x & = &-3\\\Leftrightarrow & \color{red}{-19}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-3}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{3}{19} } & & \\ & V = \left\{ \frac{3}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{+11}& = & -5 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{+11}\color{blue}{-11+12x } & = & -5 \color{red}{ -12x }\color{blue}{-11+12x } \\\Leftrightarrow & 5x \color{blue}{+12x } & = & -5 \color{blue}{-11} \\\Leftrightarrow &17x & = &-16\\\Leftrightarrow & \color{red}{17}x & = &-16\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-16}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{17} } & & \\ & V = \left\{ \frac{-16}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{+15}& = & -13 \color{red}{ +10x } \\\Leftrightarrow & 13x \color{red}{+15}\color{blue}{-15-10x } & = & -13 \color{red}{ +10x }\color{blue}{-15-10x } \\\Leftrightarrow & 13x \color{blue}{-10x } & = & -13 \color{blue}{-15} \\\Leftrightarrow &3x & = &-28\\\Leftrightarrow & \color{red}{3}x & = &-28\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-28}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-28}{3} } & & \\ & V = \left\{ \frac{-28}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{+1}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+1}\color{blue}{-1-x } & = & -5 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -5 \color{blue}{-1} \\\Leftrightarrow &-15x & = &-6\\\Leftrightarrow & \color{red}{-15}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)