Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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