Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{+10}& = & 14 \color{red}{ -2x } \\\Leftrightarrow & x \color{red}{+10}\color{blue}{-10+2x } & = & 14 \color{red}{ -2x }\color{blue}{-10+2x } \\\Leftrightarrow & x \color{blue}{+2x } & = & 14 \color{blue}{-10} \\\Leftrightarrow &3x & = &4\\\Leftrightarrow & \color{red}{3}x & = &4\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{4}{3} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{-6}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{-6}\color{blue}{+6-x } & = & 9 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & 9 \color{blue}{+6} \\\Leftrightarrow &8x & = &15\\\Leftrightarrow & \color{red}{8}x & = &15\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{15}{8} \\\Leftrightarrow & \color{green}{ x = \frac{15}{8} } & & \\ & V = \left\{ \frac{15}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{+12}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+12}\color{blue}{-12-x } & = & -15 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -15 \color{blue}{-12} \\\Leftrightarrow &-13x & = &-27\\\Leftrightarrow & \color{red}{-13}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-27}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{27}{13} } & & \\ & V = \left\{ \frac{27}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{-7}& = & 2 \color{red}{ +13x } \\\Leftrightarrow & -x \color{red}{-7}\color{blue}{+7-13x } & = & 2 \color{red}{ +13x }\color{blue}{+7-13x } \\\Leftrightarrow & -x \color{blue}{-13x } & = & 2 \color{blue}{+7} \\\Leftrightarrow &-14x & = &9\\\Leftrightarrow & \color{red}{-14}x & = &9\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{9}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{14} } & & \\ & V = \left\{ \frac{-9}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{+6}& = & 3 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+6}\color{blue}{-6+11x } & = & 3 \color{red}{ -11x }\color{blue}{-6+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 3 \color{blue}{-6} \\\Leftrightarrow &17x & = &-3\\\Leftrightarrow & \color{red}{17}x & = &-3\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-3}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{17} } & & \\ & V = \left\{ \frac{-3}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{+15}& = & -4 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+15}\color{blue}{-15+7x } & = & -4 \color{red}{ -7x }\color{blue}{-15+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & -4 \color{blue}{-15} \\\Leftrightarrow &11x & = &-19\\\Leftrightarrow & \color{red}{11}x & = &-19\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-19}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{11} } & & \\ & V = \left\{ \frac{-19}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{-11}& = & -3 \color{red}{ +14x } \\\Leftrightarrow & x \color{red}{-11}\color{blue}{+11-14x } & = & -3 \color{red}{ +14x }\color{blue}{+11-14x } \\\Leftrightarrow & x \color{blue}{-14x } & = & -3 \color{blue}{+11} \\\Leftrightarrow &-13x & = &8\\\Leftrightarrow & \color{red}{-13}x & = &8\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{8}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{13} } & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{+6}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+6}\color{blue}{-6-x } & = & 8 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 8 \color{blue}{-6} \\\Leftrightarrow &-13x & = &2\\\Leftrightarrow & \color{red}{-13}x & = &2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{13} } & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{+11}& = & -15 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{+11}\color{blue}{-11+12x } & = & -15 \color{red}{ -12x }\color{blue}{-11+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & -15 \color{blue}{-11} \\\Leftrightarrow &25x & = &-26\\\Leftrightarrow & \color{red}{25}x & = &-26\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-26}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{25} } & & \\ & V = \left\{ \frac{-26}{25} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{-14}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-14}\color{blue}{+14-x } & = & -9 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -9 \color{blue}{+14} \\\Leftrightarrow &x & = &5\\\Leftrightarrow & \color{red}{}x & = &5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 5 \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{-7}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-7}\color{blue}{+7-x } & = & 14 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 14 \color{blue}{+7} \\\Leftrightarrow &-7x & = &21\\\Leftrightarrow & \color{red}{-7}x & = &21\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{21}{-7} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{-6}& = & 8 \color{red}{ +14x } \\\Leftrightarrow & 11x \color{red}{-6}\color{blue}{+6-14x } & = & 8 \color{red}{ +14x }\color{blue}{+6-14x } \\\Leftrightarrow & 11x \color{blue}{-14x } & = & 8 \color{blue}{+6} \\\Leftrightarrow &-3x & = &14\\\Leftrightarrow & \color{red}{-3}x & = &14\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{14}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{3} } & & \\ & V = \left\{ \frac{-14}{3} \right\} & \\\end{align}\)