Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{+10}& = & 2 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{+10}\color{blue}{-10+8x } & = & 2 \color{red}{ -8x }\color{blue}{-10+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & 2 \color{blue}{-10} \\\Leftrightarrow &17x & = &-8\\\Leftrightarrow & \color{red}{17}x & = &-8\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-8}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{17} } & & \\ & V = \left\{ \frac{-8}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{-1}& = & 12 \color{red}{ +3x } \\\Leftrightarrow & 8x \color{red}{-1}\color{blue}{+1-3x } & = & 12 \color{red}{ +3x }\color{blue}{+1-3x } \\\Leftrightarrow & 8x \color{blue}{-3x } & = & 12 \color{blue}{+1} \\\Leftrightarrow &5x & = &13\\\Leftrightarrow & \color{red}{5}x & = &13\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{13}{5} \\\Leftrightarrow & \color{green}{ x = \frac{13}{5} } & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{+3}& = & 3 \color{red}{ +7x } \\\Leftrightarrow & 9x \color{red}{+3}\color{blue}{-3-7x } & = & 3 \color{red}{ +7x }\color{blue}{-3-7x } \\\Leftrightarrow & 9x \color{blue}{-7x } & = & 3 \color{blue}{-3} \\\Leftrightarrow &2x & = &0\\\Leftrightarrow & \color{red}{2}x & = &0\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{0}{2} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{-4}& = & -6 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-4}\color{blue}{+4-13x } & = & -6 \color{red}{ +13x }\color{blue}{+4-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -6 \color{blue}{+4} \\\Leftrightarrow &-25x & = &-2\\\Leftrightarrow & \color{red}{-25}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-2}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{2}{25} } & & \\ & V = \left\{ \frac{2}{25} \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{+13}& = & -3 \color{red}{ +3x } \\\Leftrightarrow & 7x \color{red}{+13}\color{blue}{-13-3x } & = & -3 \color{red}{ +3x }\color{blue}{-13-3x } \\\Leftrightarrow & 7x \color{blue}{-3x } & = & -3 \color{blue}{-13} \\\Leftrightarrow &4x & = &-16\\\Leftrightarrow & \color{red}{4}x & = &-16\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-16}{4} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{-5}& = & -14 \color{red}{ +13x } \\\Leftrightarrow & 2x \color{red}{-5}\color{blue}{+5-13x } & = & -14 \color{red}{ +13x }\color{blue}{+5-13x } \\\Leftrightarrow & 2x \color{blue}{-13x } & = & -14 \color{blue}{+5} \\\Leftrightarrow &-11x & = &-9\\\Leftrightarrow & \color{red}{-11}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 6x \color{red}{+4}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+4}\color{blue}{-4-x } & = & 12 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 12 \color{blue}{-4} \\\Leftrightarrow &5x & = &8\\\Leftrightarrow & \color{red}{5}x & = &8\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{8}{5} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{-14}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & 9x \color{red}{-14}\color{blue}{+14-13x } & = & 3 \color{red}{ +13x }\color{blue}{+14-13x } \\\Leftrightarrow & 9x \color{blue}{-13x } & = & 3 \color{blue}{+14} \\\Leftrightarrow &-4x & = &17\\\Leftrightarrow & \color{red}{-4}x & = &17\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{17}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{4} } & & \\ & V = \left\{ \frac{-17}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{+13}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+13}\color{blue}{-13-x } & = & 6 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 6 \color{blue}{-13} \\\Leftrightarrow &-5x & = &-7\\\Leftrightarrow & \color{red}{-5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{+7}& = & 3 \color{red}{ +11x } \\\Leftrightarrow & 14x \color{red}{+7}\color{blue}{-7-11x } & = & 3 \color{red}{ +11x }\color{blue}{-7-11x } \\\Leftrightarrow & 14x \color{blue}{-11x } & = & 3 \color{blue}{-7} \\\Leftrightarrow &3x & = &-4\\\Leftrightarrow & \color{red}{3}x & = &-4\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-4}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{+12}& = & 6 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+12}\color{blue}{-12-7x } & = & 6 \color{red}{ +7x }\color{blue}{-12-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 6 \color{blue}{-12} \\\Leftrightarrow &-17x & = &-6\\\Leftrightarrow & \color{red}{-17}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-6}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{6}{17} } & & \\ & V = \left\{ \frac{6}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{-3}& = & 3 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{-3}\color{blue}{+3-5x } & = & 3 \color{red}{ +5x }\color{blue}{+3-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & 3 \color{blue}{+3} \\\Leftrightarrow &-14x & = &6\\\Leftrightarrow & \color{red}{-14}x & = &6\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{6}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)