Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{+2}& = & -13 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{+2}\color{blue}{-2-12x } & = & -13 \color{red}{ +12x }\color{blue}{-2-12x } \\\Leftrightarrow & 11x \color{blue}{-12x } & = & -13 \color{blue}{-2} \\\Leftrightarrow &-x & = &-15\\\Leftrightarrow & \color{red}{-}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-15}{-1} \\\Leftrightarrow & \color{green}{ x = 15 } & & \\ & V = \left\{ 15 \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{-2}& = & -7 \color{red}{ -11x } \\\Leftrightarrow & -x \color{red}{-2}\color{blue}{+2+11x } & = & -7 \color{red}{ -11x }\color{blue}{+2+11x } \\\Leftrightarrow & -x \color{blue}{+11x } & = & -7 \color{blue}{+2} \\\Leftrightarrow &10x & = &-5\\\Leftrightarrow & \color{red}{10}x & = &-5\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-5}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{-8}& = & -9 \color{red}{ +11x } \\\Leftrightarrow & 7x \color{red}{-8}\color{blue}{+8-11x } & = & -9 \color{red}{ +11x }\color{blue}{+8-11x } \\\Leftrightarrow & 7x \color{blue}{-11x } & = & -9 \color{blue}{+8} \\\Leftrightarrow &-4x & = &-1\\\Leftrightarrow & \color{red}{-4}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{-13}& = & -1 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{-13}\color{blue}{+13-4x } & = & -1 \color{red}{ +4x }\color{blue}{+13-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & -1 \color{blue}{+13} \\\Leftrightarrow &-11x & = &12\\\Leftrightarrow & \color{red}{-11}x & = &12\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{12}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{11} } & & \\ & V = \left\{ \frac{-12}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{-2}& = & -6 \color{red}{ +11x } \\\Leftrightarrow & -13x \color{red}{-2}\color{blue}{+2-11x } & = & -6 \color{red}{ +11x }\color{blue}{+2-11x } \\\Leftrightarrow & -13x \color{blue}{-11x } & = & -6 \color{blue}{+2} \\\Leftrightarrow &-24x & = &-4\\\Leftrightarrow & \color{red}{-24}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-24}x}{ \color{blue}{ -24}} & = & \frac{-4}{-24} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{+9}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+9}\color{blue}{-9-x } & = & -2 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -2 \color{blue}{-9} \\\Leftrightarrow &-13x & = &-11\\\Leftrightarrow & \color{red}{-13}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-11}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{11}{13} } & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{+13}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+13}\color{blue}{-13-x } & = & -14 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -14 \color{blue}{-13} \\\Leftrightarrow &x & = &-27\\\Leftrightarrow & \color{red}{}x & = &-27\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -27 \\\Leftrightarrow & \color{green}{ x = -27 } & & \\ & V = \left\{ -27 \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{-13}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-13}\color{blue}{+13-x } & = & 13 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 13 \color{blue}{+13} \\\Leftrightarrow &-16x & = &26\\\Leftrightarrow & \color{red}{-16}x & = &26\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{26}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{8} } & & \\ & V = \left\{ \frac{-13}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{-15}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-15}\color{blue}{+15-x } & = & 13 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 13 \color{blue}{+15} \\\Leftrightarrow &-6x & = &28\\\Leftrightarrow & \color{red}{-6}x & = &28\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{28}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{3} } & & \\ & V = \left\{ \frac{-14}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{+10}& = & 10 \color{red}{ +4x } \\\Leftrightarrow & 7x \color{red}{+10}\color{blue}{-10-4x } & = & 10 \color{red}{ +4x }\color{blue}{-10-4x } \\\Leftrightarrow & 7x \color{blue}{-4x } & = & 10 \color{blue}{-10} \\\Leftrightarrow &3x & = &0\\\Leftrightarrow & \color{red}{3}x & = &0\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{0}{3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{-15}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-15}\color{blue}{+15-x } & = & 9 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 9 \color{blue}{+15} \\\Leftrightarrow &-5x & = &24\\\Leftrightarrow & \color{red}{-5}x & = &24\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{24}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{5} } & & \\ & V = \left\{ \frac{-24}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{+1}& = & -12 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{+1}\color{blue}{-1-11x } & = & -12 \color{red}{ +11x }\color{blue}{-1-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & -12 \color{blue}{-1} \\\Leftrightarrow &x & = &-13\\\Leftrightarrow & \color{red}{}x & = &-13\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -13 \\\Leftrightarrow & \color{green}{ x = -13 } & & \\ & V = \left\{ -13 \right\} & \\\end{align}\)