Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{-7}& = & -3 \color{red}{ +9x } \\\Leftrightarrow & -x \color{red}{-7}\color{blue}{+7-9x } & = & -3 \color{red}{ +9x }\color{blue}{+7-9x } \\\Leftrightarrow & -x \color{blue}{-9x } & = & -3 \color{blue}{+7} \\\Leftrightarrow &-10x & = &4\\\Leftrightarrow & \color{red}{-10}x & = &4\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{4}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{-1}& = & -3 \color{red}{ +13x } \\\Leftrightarrow & 11x \color{red}{-1}\color{blue}{+1-13x } & = & -3 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & 11x \color{blue}{-13x } & = & -3 \color{blue}{+1} \\\Leftrightarrow &-2x & = &-2\\\Leftrightarrow & \color{red}{-2}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-2}{-2} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{+12}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+12}\color{blue}{-12-x } & = & 5 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 5 \color{blue}{-12} \\\Leftrightarrow &-4x & = &-7\\\Leftrightarrow & \color{red}{-4}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-7}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{-7}& = & 10 \color{red}{ -2x } \\\Leftrightarrow & 9x \color{red}{-7}\color{blue}{+7+2x } & = & 10 \color{red}{ -2x }\color{blue}{+7+2x } \\\Leftrightarrow & 9x \color{blue}{+2x } & = & 10 \color{blue}{+7} \\\Leftrightarrow &11x & = &17\\\Leftrightarrow & \color{red}{11}x & = &17\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{17}{11} \\\Leftrightarrow & \color{green}{ x = \frac{17}{11} } & & \\ & V = \left\{ \frac{17}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{+1}& = & 2 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{+1}\color{blue}{-1+11x } & = & 2 \color{red}{ -11x }\color{blue}{-1+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & 2 \color{blue}{-1} \\\Leftrightarrow &14x & = &1\\\Leftrightarrow & \color{red}{14}x & = &1\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{1}{14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{14} } & & \\ & V = \left\{ \frac{1}{14} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{+6}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+6}\color{blue}{-6-x } & = & -2 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -2 \color{blue}{-6} \\\Leftrightarrow &-12x & = &-8\\\Leftrightarrow & \color{red}{-12}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-8}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{+7}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+7}\color{blue}{-7-x } & = & -2 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -2 \color{blue}{-7} \\\Leftrightarrow &11x & = &-9\\\Leftrightarrow & \color{red}{11}x & = &-9\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-9}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{11} } & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{+13}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+13}\color{blue}{-13-13x } & = & -10 \color{red}{ +13x }\color{blue}{-13-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -10 \color{blue}{-13} \\\Leftrightarrow &-28x & = &-23\\\Leftrightarrow & \color{red}{-28}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-23}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{23}{28} } & & \\ & V = \left\{ \frac{23}{28} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{-13}& = & -8 \color{red}{ +13x } \\\Leftrightarrow & -2x \color{red}{-13}\color{blue}{+13-13x } & = & -8 \color{red}{ +13x }\color{blue}{+13-13x } \\\Leftrightarrow & -2x \color{blue}{-13x } & = & -8 \color{blue}{+13} \\\Leftrightarrow &-15x & = &5\\\Leftrightarrow & \color{red}{-15}x & = &5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{-14}& = & 1 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-14}\color{blue}{+14+3x } & = & 1 \color{red}{ -3x }\color{blue}{+14+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 1 \color{blue}{+14} \\\Leftrightarrow &13x & = &15\\\Leftrightarrow & \color{red}{13}x & = &15\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{15}{13} \\\Leftrightarrow & \color{green}{ x = \frac{15}{13} } & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{-15}& = & 8 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-15}\color{blue}{+15+13x } & = & 8 \color{red}{ -13x }\color{blue}{+15+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 8 \color{blue}{+15} \\\Leftrightarrow &27x & = &23\\\Leftrightarrow & \color{red}{27}x & = &23\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{23}{27} \\\Leftrightarrow & \color{green}{ x = \frac{23}{27} } & & \\ & V = \left\{ \frac{23}{27} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{+7}& = & 12 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{+7}\color{blue}{-7-6x } & = & 12 \color{red}{ +6x }\color{blue}{-7-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & 12 \color{blue}{-7} \\\Leftrightarrow &-11x & = &5\\\Leftrightarrow & \color{red}{-11}x & = &5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)