Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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