Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{+13}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+13}\color{blue}{-13-x } & = & -13 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -13 \color{blue}{-13} \\\Leftrightarrow &-15x & = &-26\\\Leftrightarrow & \color{red}{-15}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-26}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{26}{15} } & & \\ & V = \left\{ \frac{26}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{+3}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+3}\color{blue}{-3-x } & = & -14 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -14 \color{blue}{-3} \\\Leftrightarrow &11x & = &-17\\\Leftrightarrow & \color{red}{11}x & = &-17\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-17}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{11} } & & \\ & V = \left\{ \frac{-17}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{-5}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-5}\color{blue}{+5-13x } & = & -10 \color{red}{ +13x }\color{blue}{+5-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -10 \color{blue}{+5} \\\Leftrightarrow &-19x & = &-5\\\Leftrightarrow & \color{red}{-19}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-5}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{5}{19} } & & \\ & V = \left\{ \frac{5}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{-15}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-15}\color{blue}{+15-x } & = & -2 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -2 \color{blue}{+15} \\\Leftrightarrow &-11x & = &13\\\Leftrightarrow & \color{red}{-11}x & = &13\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{13}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{11} } & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{+5}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+5}\color{blue}{-5-x } & = & -9 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -9 \color{blue}{-5} \\\Leftrightarrow &-12x & = &-14\\\Leftrightarrow & \color{red}{-12}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-14}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{6} } & & \\ & V = \left\{ \frac{7}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{+13}& = & 3 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+13}\color{blue}{-13+11x } & = & 3 \color{red}{ -11x }\color{blue}{-13+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 3 \color{blue}{-13} \\\Leftrightarrow &17x & = &-10\\\Leftrightarrow & \color{red}{17}x & = &-10\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-10}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{17} } & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{-5}& = & 15 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{-5}\color{blue}{+5-5x } & = & 15 \color{red}{ +5x }\color{blue}{+5-5x } \\\Leftrightarrow & -2x \color{blue}{-5x } & = & 15 \color{blue}{+5} \\\Leftrightarrow &-7x & = &20\\\Leftrightarrow & \color{red}{-7}x & = &20\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{20}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{7} } & & \\ & V = \left\{ \frac{-20}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{+14}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & 14x \color{red}{+14}\color{blue}{-14-13x } & = & 14 \color{red}{ +13x }\color{blue}{-14-13x } \\\Leftrightarrow & 14x \color{blue}{-13x } & = & 14 \color{blue}{-14} \\\Leftrightarrow &x & = &0\\\Leftrightarrow & \color{red}{}x & = &0\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 0 \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{-5}& = & 5 \color{red}{ +6x } \\\Leftrightarrow & x \color{red}{-5}\color{blue}{+5-6x } & = & 5 \color{red}{ +6x }\color{blue}{+5-6x } \\\Leftrightarrow & x \color{blue}{-6x } & = & 5 \color{blue}{+5} \\\Leftrightarrow &-5x & = &10\\\Leftrightarrow & \color{red}{-5}x & = &10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{10}{-5} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{-12}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-12}\color{blue}{+12-x } & = & 9 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 9 \color{blue}{+12} \\\Leftrightarrow &-6x & = &21\\\Leftrightarrow & \color{red}{-6}x & = &21\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{21}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{+7}& = & -10 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+7}\color{blue}{-7+6x } & = & -10 \color{red}{ -6x }\color{blue}{-7+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -10 \color{blue}{-7} \\\Leftrightarrow &19x & = &-17\\\Leftrightarrow & \color{red}{19}x & = &-17\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-17}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{19} } & & \\ & V = \left\{ \frac{-17}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{+3}& = & -6 \color{red}{ +14x } \\\Leftrightarrow & 9x \color{red}{+3}\color{blue}{-3-14x } & = & -6 \color{red}{ +14x }\color{blue}{-3-14x } \\\Leftrightarrow & 9x \color{blue}{-14x } & = & -6 \color{blue}{-3} \\\Leftrightarrow &-5x & = &-9\\\Leftrightarrow & \color{red}{-5}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-9}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)