Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{-2}& = & -12 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{-2}\color{blue}{+2-11x } & = & -12 \color{red}{ +11x }\color{blue}{+2-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & -12 \color{blue}{+2} \\\Leftrightarrow &-21x & = &-10\\\Leftrightarrow & \color{red}{-21}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{-10}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{10}{21} } & & \\ & V = \left\{ \frac{10}{21} \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{-3}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-3}\color{blue}{+3-x } & = & -2 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -2 \color{blue}{+3} \\\Leftrightarrow &x & = &1\\\Leftrightarrow & \color{red}{}x & = &1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 1 \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{-14}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-14}\color{blue}{+14-x } & = & -5 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -5 \color{blue}{+14} \\\Leftrightarrow &-3x & = &9\\\Leftrightarrow & \color{red}{-3}x & = &9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{9}{-3} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
4. \(\begin{align} & x \color{red}{-11}& = & 4 \color{red}{ -4x } \\\Leftrightarrow & x \color{red}{-11}\color{blue}{+11+4x } & = & 4 \color{red}{ -4x }\color{blue}{+11+4x } \\\Leftrightarrow & x \color{blue}{+4x } & = & 4 \color{blue}{+11} \\\Leftrightarrow &5x & = &15\\\Leftrightarrow & \color{red}{5}x & = &15\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{15}{5} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{-14}& = & 4 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{-14}\color{blue}{+14-12x } & = & 4 \color{red}{ +12x }\color{blue}{+14-12x } \\\Leftrightarrow & -11x \color{blue}{-12x } & = & 4 \color{blue}{+14} \\\Leftrightarrow &-23x & = &18\\\Leftrightarrow & \color{red}{-23}x & = &18\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{18}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{23} } & & \\ & V = \left\{ \frac{-18}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{+13}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+13}\color{blue}{-13-x } & = & -2 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -2 \color{blue}{-13} \\\Leftrightarrow &x & = &-15\\\Leftrightarrow & \color{red}{}x & = &-15\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -15 \\\Leftrightarrow & \color{green}{ x = -15 } & & \\ & V = \left\{ -15 \right\} & \\\end{align}\)
7. \(\begin{align} & 6x \color{red}{-13}& = & 12 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{-13}\color{blue}{+13-11x } & = & 12 \color{red}{ +11x }\color{blue}{+13-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & 12 \color{blue}{+13} \\\Leftrightarrow &-5x & = &25\\\Leftrightarrow & \color{red}{-5}x & = &25\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{25}{-5} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{-13}& = & -15 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{-13}\color{blue}{+13+4x } & = & -15 \color{red}{ -4x }\color{blue}{+13+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & -15 \color{blue}{+13} \\\Leftrightarrow &9x & = &-2\\\Leftrightarrow & \color{red}{9}x & = &-2\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-2}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{+3}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+3}\color{blue}{-3-x } & = & -10 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -10 \color{blue}{-3} \\\Leftrightarrow &-8x & = &-13\\\Leftrightarrow & \color{red}{-8}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-13}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{13}{8} } & & \\ & V = \left\{ \frac{13}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{-13}& = & -12 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{-13}\color{blue}{+13-11x } & = & -12 \color{red}{ +11x }\color{blue}{+13-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & -12 \color{blue}{+13} \\\Leftrightarrow &-21x & = &1\\\Leftrightarrow & \color{red}{-21}x & = &1\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{1}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{21} } & & \\ & V = \left\{ \frac{-1}{21} \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{-8}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{-8}\color{blue}{+8-x } & = & -6 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & -6 \color{blue}{+8} \\\Leftrightarrow &4x & = &2\\\Leftrightarrow & \color{red}{4}x & = &2\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{2}{4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{+11}& = & 13 \color{red}{ +7x } \\\Leftrightarrow & 9x \color{red}{+11}\color{blue}{-11-7x } & = & 13 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & 9x \color{blue}{-7x } & = & 13 \color{blue}{-11} \\\Leftrightarrow &2x & = &2\\\Leftrightarrow & \color{red}{2}x & = &2\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{2}{2} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)