Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{-15}& = & 8 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{-15}\color{blue}{+15-7x } & = & 8 \color{red}{ +7x }\color{blue}{+15-7x } \\\Leftrightarrow & 3x \color{blue}{-7x } & = & 8 \color{blue}{+15} \\\Leftrightarrow &-4x & = &23\\\Leftrightarrow & \color{red}{-4}x & = &23\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{23}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{4} } & & \\ & V = \left\{ \frac{-23}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{-6}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{-6}\color{blue}{+6-13x } & = & 3 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & 3 \color{blue}{+6} \\\Leftrightarrow &-17x & = &9\\\Leftrightarrow & \color{red}{-17}x & = &9\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{9}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{17} } & & \\ & V = \left\{ \frac{-9}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{+4}& = & -12 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{+4}\color{blue}{-4-7x } & = & -12 \color{red}{ +7x }\color{blue}{-4-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & -12 \color{blue}{-4} \\\Leftrightarrow &-5x & = &-16\\\Leftrightarrow & \color{red}{-5}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-16}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{16}{5} } & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{-3}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-3}\color{blue}{+3-x } & = & 4 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 4 \color{blue}{+3} \\\Leftrightarrow &-6x & = &7\\\Leftrightarrow & \color{red}{-6}x & = &7\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{7}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{6} } & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{-13}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-13}\color{blue}{+13-x } & = & 4 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 4 \color{blue}{+13} \\\Leftrightarrow &-4x & = &17\\\Leftrightarrow & \color{red}{-4}x & = &17\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{17}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{4} } & & \\ & V = \left\{ \frac{-17}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{+7}& = & 9 \color{red}{ +7x } \\\Leftrightarrow & -2x \color{red}{+7}\color{blue}{-7-7x } & = & 9 \color{red}{ +7x }\color{blue}{-7-7x } \\\Leftrightarrow & -2x \color{blue}{-7x } & = & 9 \color{blue}{-7} \\\Leftrightarrow &-9x & = &2\\\Leftrightarrow & \color{red}{-9}x & = &2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{+13}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+13}\color{blue}{-13-x } & = & -15 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -15 \color{blue}{-13} \\\Leftrightarrow &-15x & = &-28\\\Leftrightarrow & \color{red}{-15}x & = &-28\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-28}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{28}{15} } & & \\ & V = \left\{ \frac{28}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{+15}& = & -1 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+15}\color{blue}{-15+13x } & = & -1 \color{red}{ -13x }\color{blue}{-15+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & -1 \color{blue}{-15} \\\Leftrightarrow &24x & = &-16\\\Leftrightarrow & \color{red}{24}x & = &-16\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-16}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{+15}& = & 3 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+15}\color{blue}{-15-7x } & = & 3 \color{red}{ +7x }\color{blue}{-15-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 3 \color{blue}{-15} \\\Leftrightarrow &-20x & = &-12\\\Leftrightarrow & \color{red}{-20}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-12}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{-3}& = & 1 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-3}\color{blue}{+3-7x } & = & 1 \color{red}{ +7x }\color{blue}{+3-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 1 \color{blue}{+3} \\\Leftrightarrow &-17x & = &4\\\Leftrightarrow & \color{red}{-17}x & = &4\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{4}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{17} } & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{-12}& = & -5 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-12}\color{blue}{+12-13x } & = & -5 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -5 \color{blue}{+12} \\\Leftrightarrow &-19x & = &7\\\Leftrightarrow & \color{red}{-19}x & = &7\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{7}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{19} } & & \\ & V = \left\{ \frac{-7}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{-12}& = & -11 \color{red}{ +7x } \\\Leftrightarrow & 4x \color{red}{-12}\color{blue}{+12-7x } & = & -11 \color{red}{ +7x }\color{blue}{+12-7x } \\\Leftrightarrow & 4x \color{blue}{-7x } & = & -11 \color{blue}{+12} \\\Leftrightarrow &-3x & = &1\\\Leftrightarrow & \color{red}{-3}x & = &1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)