Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{-15}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-15}\color{blue}{+15-x } & = & 1 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 1 \color{blue}{+15} \\\Leftrightarrow &13x & = &16\\\Leftrightarrow & \color{red}{13}x & = &16\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{16}{13} \\\Leftrightarrow & \color{green}{ x = \frac{16}{13} } & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{+12}& = & 11 \color{red}{ +8x } \\\Leftrightarrow & 3x \color{red}{+12}\color{blue}{-12-8x } & = & 11 \color{red}{ +8x }\color{blue}{-12-8x } \\\Leftrightarrow & 3x \color{blue}{-8x } & = & 11 \color{blue}{-12} \\\Leftrightarrow &-5x & = &-1\\\Leftrightarrow & \color{red}{-5}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{-1}& = & -6 \color{red}{ +8x } \\\Leftrightarrow & 15x \color{red}{-1}\color{blue}{+1-8x } & = & -6 \color{red}{ +8x }\color{blue}{+1-8x } \\\Leftrightarrow & 15x \color{blue}{-8x } & = & -6 \color{blue}{+1} \\\Leftrightarrow &7x & = &-5\\\Leftrightarrow & \color{red}{7}x & = &-5\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-5}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{-7}& = & 9 \color{red}{ +11x } \\\Leftrightarrow & 9x \color{red}{-7}\color{blue}{+7-11x } & = & 9 \color{red}{ +11x }\color{blue}{+7-11x } \\\Leftrightarrow & 9x \color{blue}{-11x } & = & 9 \color{blue}{+7} \\\Leftrightarrow &-2x & = &16\\\Leftrightarrow & \color{red}{-2}x & = &16\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{16}{-2} \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{+10}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & -2x \color{red}{+10}\color{blue}{-10-13x } & = & -7 \color{red}{ +13x }\color{blue}{-10-13x } \\\Leftrightarrow & -2x \color{blue}{-13x } & = & -7 \color{blue}{-10} \\\Leftrightarrow &-15x & = &-17\\\Leftrightarrow & \color{red}{-15}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-17}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{17}{15} } & & \\ & V = \left\{ \frac{17}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{-12}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-12}\color{blue}{+12-x } & = & 15 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 15 \color{blue}{+12} \\\Leftrightarrow &-14x & = &27\\\Leftrightarrow & \color{red}{-14}x & = &27\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{27}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{14} } & & \\ & V = \left\{ \frac{-27}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{+15}& = & 9 \color{red}{ -10x } \\\Leftrightarrow & x \color{red}{+15}\color{blue}{-15+10x } & = & 9 \color{red}{ -10x }\color{blue}{-15+10x } \\\Leftrightarrow & x \color{blue}{+10x } & = & 9 \color{blue}{-15} \\\Leftrightarrow &11x & = &-6\\\Leftrightarrow & \color{red}{11}x & = &-6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{+8}& = & -6 \color{red}{ -14x } \\\Leftrightarrow & 3x \color{red}{+8}\color{blue}{-8+14x } & = & -6 \color{red}{ -14x }\color{blue}{-8+14x } \\\Leftrightarrow & 3x \color{blue}{+14x } & = & -6 \color{blue}{-8} \\\Leftrightarrow &17x & = &-14\\\Leftrightarrow & \color{red}{17}x & = &-14\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-14}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{17} } & & \\ & V = \left\{ \frac{-14}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{+2}& = & -1 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+2}\color{blue}{-2+13x } & = & -1 \color{red}{ -13x }\color{blue}{-2+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -1 \color{blue}{-2} \\\Leftrightarrow &27x & = &-3\\\Leftrightarrow & \color{red}{27}x & = &-3\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-3}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{9} } & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{+5}& = & -6 \color{red}{ +13x } \\\Leftrightarrow & 5x \color{red}{+5}\color{blue}{-5-13x } & = & -6 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & 5x \color{blue}{-13x } & = & -6 \color{blue}{-5} \\\Leftrightarrow &-8x & = &-11\\\Leftrightarrow & \color{red}{-8}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-11}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{11}{8} } & & \\ & V = \left\{ \frac{11}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{+13}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{+13}\color{blue}{-13-x } & = & 10 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & 10 \color{blue}{-13} \\\Leftrightarrow &2x & = &-3\\\Leftrightarrow & \color{red}{2}x & = &-3\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-3}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{-3}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-3}\color{blue}{+3-x } & = & 3 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 3 \color{blue}{+3} \\\Leftrightarrow &-4x & = &6\\\Leftrightarrow & \color{red}{-4}x & = &6\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{6}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)