Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{-6}& = & -6 \color{red}{ +7x } \\\Leftrightarrow & 5x \color{red}{-6}\color{blue}{+6-7x } & = & -6 \color{red}{ +7x }\color{blue}{+6-7x } \\\Leftrightarrow & 5x \color{blue}{-7x } & = & -6 \color{blue}{+6} \\\Leftrightarrow &-2x & = &0\\\Leftrightarrow & \color{red}{-2}x & = &0\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{0}{-2} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{+4}& = & 12 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{+4}\color{blue}{-4-10x } & = & 12 \color{red}{ +10x }\color{blue}{-4-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & 12 \color{blue}{-4} \\\Leftrightarrow &-13x & = &8\\\Leftrightarrow & \color{red}{-13}x & = &8\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{8}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{13} } & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{+5}& = & 1 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{+5}\color{blue}{-5+3x } & = & 1 \color{red}{ -3x }\color{blue}{-5+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & 1 \color{blue}{-5} \\\Leftrightarrow &10x & = &-4\\\Leftrightarrow & \color{red}{10}x & = &-4\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-4}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-3}& = & 2 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-3}\color{blue}{+3-13x } & = & 2 \color{red}{ +13x }\color{blue}{+3-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 2 \color{blue}{+3} \\\Leftrightarrow &-28x & = &5\\\Leftrightarrow & \color{red}{-28}x & = &5\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{5}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{28} } & & \\ & V = \left\{ \frac{-5}{28} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{-14}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-14}\color{blue}{+14-x } & = & 5 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 5 \color{blue}{+14} \\\Leftrightarrow &-6x & = &19\\\Leftrightarrow & \color{red}{-6}x & = &19\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{19}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{6} } & & \\ & V = \left\{ \frac{-19}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{-12}& = & 7 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{-12}\color{blue}{+12+7x } & = & 7 \color{red}{ -7x }\color{blue}{+12+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & 7 \color{blue}{+12} \\\Leftrightarrow &19x & = &19\\\Leftrightarrow & \color{red}{19}x & = &19\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{19}{19} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{-1}& = & -15 \color{red}{ +14x } \\\Leftrightarrow & 15x \color{red}{-1}\color{blue}{+1-14x } & = & -15 \color{red}{ +14x }\color{blue}{+1-14x } \\\Leftrightarrow & 15x \color{blue}{-14x } & = & -15 \color{blue}{+1} \\\Leftrightarrow &x & = &-14\\\Leftrightarrow & \color{red}{}x & = &-14\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -14 \\\Leftrightarrow & \color{green}{ x = -14 } & & \\ & V = \left\{ -14 \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+13}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+13}\color{blue}{-13-x } & = & -6 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -6 \color{blue}{-13} \\\Leftrightarrow &-11x & = &-19\\\Leftrightarrow & \color{red}{-11}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-19}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{19}{11} } & & \\ & V = \left\{ \frac{19}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{+2}& = & -1 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+2}\color{blue}{-2+5x } & = & -1 \color{red}{ -5x }\color{blue}{-2+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & -1 \color{blue}{-2} \\\Leftrightarrow &11x & = &-3\\\Leftrightarrow & \color{red}{11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-3}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{+11}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+11}\color{blue}{-11-x } & = & 6 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 6 \color{blue}{-11} \\\Leftrightarrow &-11x & = &-5\\\Leftrightarrow & \color{red}{-11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{+13}& = & 5 \color{red}{ +15x } \\\Leftrightarrow & -x \color{red}{+13}\color{blue}{-13-15x } & = & 5 \color{red}{ +15x }\color{blue}{-13-15x } \\\Leftrightarrow & -x \color{blue}{-15x } & = & 5 \color{blue}{-13} \\\Leftrightarrow &-16x & = &-8\\\Leftrightarrow & \color{red}{-16}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-8}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{+6}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+6}\color{blue}{-6-x } & = & -5 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -5 \color{blue}{-6} \\\Leftrightarrow &-10x & = &-11\\\Leftrightarrow & \color{red}{-10}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-11}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{11}{10} } & & \\ & V = \left\{ \frac{11}{10} \right\} & \\\end{align}\)