Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{+3}& = & -6 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{+3}\color{blue}{-3-4x } & = & -6 \color{red}{ +4x }\color{blue}{-3-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & -6 \color{blue}{-3} \\\Leftrightarrow &-7x & = &-9\\\Leftrightarrow & \color{red}{-7}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{9}{7} } & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{-14}& = & 7 \color{red}{ +3x } \\\Leftrightarrow & -14x \color{red}{-14}\color{blue}{+14-3x } & = & 7 \color{red}{ +3x }\color{blue}{+14-3x } \\\Leftrightarrow & -14x \color{blue}{-3x } & = & 7 \color{blue}{+14} \\\Leftrightarrow &-17x & = &21\\\Leftrightarrow & \color{red}{-17}x & = &21\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{21}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{17} } & & \\ & V = \left\{ \frac{-21}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{+12}& = & -8 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+12}\color{blue}{-12-7x } & = & -8 \color{red}{ +7x }\color{blue}{-12-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -8 \color{blue}{-12} \\\Leftrightarrow &-13x & = &-20\\\Leftrightarrow & \color{red}{-13}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-20}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{20}{13} } & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{+14}& = & 12 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{+14}\color{blue}{-14+12x } & = & 12 \color{red}{ -12x }\color{blue}{-14+12x } \\\Leftrightarrow & 5x \color{blue}{+12x } & = & 12 \color{blue}{-14} \\\Leftrightarrow &17x & = &-2\\\Leftrightarrow & \color{red}{17}x & = &-2\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-2}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{17} } & & \\ & V = \left\{ \frac{-2}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{+15}& = & 4 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+15}\color{blue}{-15+11x } & = & 4 \color{red}{ -11x }\color{blue}{-15+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 4 \color{blue}{-15} \\\Leftrightarrow &23x & = &-11\\\Leftrightarrow & \color{red}{23}x & = &-11\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-11}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{23} } & & \\ & V = \left\{ \frac{-11}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{-12}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 15x \color{red}{-12}\color{blue}{+12-x } & = & 4 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & 15x \color{blue}{-x } & = & 4 \color{blue}{+12} \\\Leftrightarrow &14x & = &16\\\Leftrightarrow & \color{red}{14}x & = &16\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{16}{14} \\\Leftrightarrow & \color{green}{ x = \frac{8}{7} } & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{-13}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-13}\color{blue}{+13-x } & = & -13 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -13 \color{blue}{+13} \\\Leftrightarrow &x & = &0\\\Leftrightarrow & \color{red}{}x & = &0\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 0 \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{+15}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+15}\color{blue}{-15-x } & = & 11 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 11 \color{blue}{-15} \\\Leftrightarrow &-6x & = &-4\\\Leftrightarrow & \color{red}{-6}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-4}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{-8}& = & 10 \color{red}{ +5x } \\\Leftrightarrow & x \color{red}{-8}\color{blue}{+8-5x } & = & 10 \color{red}{ +5x }\color{blue}{+8-5x } \\\Leftrightarrow & x \color{blue}{-5x } & = & 10 \color{blue}{+8} \\\Leftrightarrow &-4x & = &18\\\Leftrightarrow & \color{red}{-4}x & = &18\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{18}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{2} } & & \\ & V = \left\{ \frac{-9}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{+8}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & -2x \color{red}{+8}\color{blue}{-8-11x } & = & -3 \color{red}{ +11x }\color{blue}{-8-11x } \\\Leftrightarrow & -2x \color{blue}{-11x } & = & -3 \color{blue}{-8} \\\Leftrightarrow &-13x & = &-11\\\Leftrightarrow & \color{red}{-13}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-11}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{11}{13} } & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{+7}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+7}\color{blue}{-7-x } & = & 14 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 14 \color{blue}{-7} \\\Leftrightarrow &-12x & = &7\\\Leftrightarrow & \color{red}{-12}x & = &7\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{7}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{12} } & & \\ & V = \left\{ \frac{-7}{12} \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{+8}& = & -15 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+8}\color{blue}{-8+13x } & = & -15 \color{red}{ -13x }\color{blue}{-8+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -15 \color{blue}{-8} \\\Leftrightarrow &23x & = &-23\\\Leftrightarrow & \color{red}{23}x & = &-23\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-23}{23} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)