Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{+3}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+3}\color{blue}{-3-x } & = & -12 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -12 \color{blue}{-3} \\\Leftrightarrow &-12x & = &-15\\\Leftrightarrow & \color{red}{-12}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-15}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{-11}& = & 10 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{-11}\color{blue}{+11+11x } & = & 10 \color{red}{ -11x }\color{blue}{+11+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & 10 \color{blue}{+11} \\\Leftrightarrow &26x & = &21\\\Leftrightarrow & \color{red}{26}x & = &21\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{21}{26} \\\Leftrightarrow & \color{green}{ x = \frac{21}{26} } & & \\ & V = \left\{ \frac{21}{26} \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{-12}& = & -8 \color{red}{ +14x } \\\Leftrightarrow & -x \color{red}{-12}\color{blue}{+12-14x } & = & -8 \color{red}{ +14x }\color{blue}{+12-14x } \\\Leftrightarrow & -x \color{blue}{-14x } & = & -8 \color{blue}{+12} \\\Leftrightarrow &-15x & = &4\\\Leftrightarrow & \color{red}{-15}x & = &4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{15} } & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{+13}& = & 13 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{+13}\color{blue}{-13-7x } & = & 13 \color{red}{ +7x }\color{blue}{-13-7x } \\\Leftrightarrow & 3x \color{blue}{-7x } & = & 13 \color{blue}{-13} \\\Leftrightarrow &-4x & = &0\\\Leftrightarrow & \color{red}{-4}x & = &0\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{0}{-4} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{+14}& = & -3 \color{red}{ -x } \\\Leftrightarrow & x \color{red}{+14}\color{blue}{-14+x } & = & -3 \color{red}{ -x }\color{blue}{-14+x } \\\Leftrightarrow & x \color{blue}{+x } & = & -3 \color{blue}{-14} \\\Leftrightarrow &2x & = &-17\\\Leftrightarrow & \color{red}{2}x & = &-17\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-17}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{2} } & & \\ & V = \left\{ \frac{-17}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{-12}& = & 6 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{-12}\color{blue}{+12-11x } & = & 6 \color{red}{ +11x }\color{blue}{+12-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & 6 \color{blue}{+12} \\\Leftrightarrow &4x & = &18\\\Leftrightarrow & \color{red}{4}x & = &18\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{18}{4} \\\Leftrightarrow & \color{green}{ x = \frac{9}{2} } & & \\ & V = \left\{ \frac{9}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{+11}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+11}\color{blue}{-11-x } & = & -1 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -1 \color{blue}{-11} \\\Leftrightarrow &-13x & = &-12\\\Leftrightarrow & \color{red}{-13}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{12}{13} } & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{+9}& = & -5 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{+9}\color{blue}{-9+10x } & = & -5 \color{red}{ -10x }\color{blue}{-9+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & -5 \color{blue}{-9} \\\Leftrightarrow &21x & = &-14\\\Leftrightarrow & \color{red}{21}x & = &-14\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-14}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{-14}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-14}\color{blue}{+14-x } & = & -6 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -6 \color{blue}{+14} \\\Leftrightarrow &-11x & = &8\\\Leftrightarrow & \color{red}{-11}x & = &8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{11} } & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{-13}& = & -12 \color{red}{ +11x } \\\Leftrightarrow & 5x \color{red}{-13}\color{blue}{+13-11x } & = & -12 \color{red}{ +11x }\color{blue}{+13-11x } \\\Leftrightarrow & 5x \color{blue}{-11x } & = & -12 \color{blue}{+13} \\\Leftrightarrow &-6x & = &1\\\Leftrightarrow & \color{red}{-6}x & = &1\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{1}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{-2}& = & -5 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{-2}\color{blue}{+2-11x } & = & -5 \color{red}{ +11x }\color{blue}{+2-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & -5 \color{blue}{+2} \\\Leftrightarrow &-5x & = &-3\\\Leftrightarrow & \color{red}{-5}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{-14}& = & 5 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{-14}\color{blue}{+14-11x } & = & 5 \color{red}{ +11x }\color{blue}{+14-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & 5 \color{blue}{+14} \\\Leftrightarrow &x & = &19\\\Leftrightarrow & \color{red}{}x & = &19\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 19 \\\Leftrightarrow & \color{green}{ x = 19 } & & \\ & V = \left\{ 19 \right\} & \\\end{align}\)