Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{-11}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-11}\color{blue}{+11-x } & = & 12 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 12 \color{blue}{+11} \\\Leftrightarrow &-12x & = &23\\\Leftrightarrow & \color{red}{-12}x & = &23\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{23}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{12} } & & \\ & V = \left\{ \frac{-23}{12} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{+13}& = & 11 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+13}\color{blue}{-13+11x } & = & 11 \color{red}{ -11x }\color{blue}{-13+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & 11 \color{blue}{-13} \\\Leftrightarrow &15x & = &-2\\\Leftrightarrow & \color{red}{15}x & = &-2\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-2}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{15} } & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{-7}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-7}\color{blue}{+7-x } & = & -9 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -9 \color{blue}{+7} \\\Leftrightarrow &13x & = &-2\\\Leftrightarrow & \color{red}{13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-2}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{13} } & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{+7}& = & -8 \color{red}{ +14x } \\\Leftrightarrow & 3x \color{red}{+7}\color{blue}{-7-14x } & = & -8 \color{red}{ +14x }\color{blue}{-7-14x } \\\Leftrightarrow & 3x \color{blue}{-14x } & = & -8 \color{blue}{-7} \\\Leftrightarrow &-11x & = &-15\\\Leftrightarrow & \color{red}{-11}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-15}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{15}{11} } & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{-13}& = & 14 \color{red}{ -13x } \\\Leftrightarrow & x \color{red}{-13}\color{blue}{+13+13x } & = & 14 \color{red}{ -13x }\color{blue}{+13+13x } \\\Leftrightarrow & x \color{blue}{+13x } & = & 14 \color{blue}{+13} \\\Leftrightarrow &14x & = &27\\\Leftrightarrow & \color{red}{14}x & = &27\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{27}{14} \\\Leftrightarrow & \color{green}{ x = \frac{27}{14} } & & \\ & V = \left\{ \frac{27}{14} \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{-10}& = & 7 \color{red}{ +8x } \\\Leftrightarrow & 15x \color{red}{-10}\color{blue}{+10-8x } & = & 7 \color{red}{ +8x }\color{blue}{+10-8x } \\\Leftrightarrow & 15x \color{blue}{-8x } & = & 7 \color{blue}{+10} \\\Leftrightarrow &7x & = &17\\\Leftrightarrow & \color{red}{7}x & = &17\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{17}{7} \\\Leftrightarrow & \color{green}{ x = \frac{17}{7} } & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{-11}& = & -15 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-11}\color{blue}{+11-13x } & = & -15 \color{red}{ +13x }\color{blue}{+11-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -15 \color{blue}{+11} \\\Leftrightarrow &-28x & = &-4\\\Leftrightarrow & \color{red}{-28}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-4}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{+3}& = & -15 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{+3}\color{blue}{-3-11x } & = & -15 \color{red}{ +11x }\color{blue}{-3-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & -15 \color{blue}{-3} \\\Leftrightarrow &-18x & = &-18\\\Leftrightarrow & \color{red}{-18}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{-18}{-18} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{-9}& = & 2 \color{red}{ +13x } \\\Leftrightarrow & -x \color{red}{-9}\color{blue}{+9-13x } & = & 2 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & -x \color{blue}{-13x } & = & 2 \color{blue}{+9} \\\Leftrightarrow &-14x & = &11\\\Leftrightarrow & \color{red}{-14}x & = &11\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{11}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{14} } & & \\ & V = \left\{ \frac{-11}{14} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{-13}& = & -9 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-13}\color{blue}{+13-7x } & = & -9 \color{red}{ +7x }\color{blue}{+13-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -9 \color{blue}{+13} \\\Leftrightarrow &-13x & = &4\\\Leftrightarrow & \color{red}{-13}x & = &4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{-11}& = & -9 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{-11}\color{blue}{+11-5x } & = & -9 \color{red}{ +5x }\color{blue}{+11-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & -9 \color{blue}{+11} \\\Leftrightarrow &-17x & = &2\\\Leftrightarrow & \color{red}{-17}x & = &2\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{2}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{17} } & & \\ & V = \left\{ \frac{-2}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{+13}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+13}\color{blue}{-13-x } & = & 7 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 7 \color{blue}{-13} \\\Leftrightarrow &-11x & = &-6\\\Leftrightarrow & \color{red}{-11}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-6}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{6}{11} } & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)