Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{+11}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+11}\color{blue}{-11-x } & = & 10 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 10 \color{blue}{-11} \\\Leftrightarrow &7x & = &-1\\\Leftrightarrow & \color{red}{7}x & = &-1\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-1}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{+13}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+13}\color{blue}{-13-x } & = & -12 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -12 \color{blue}{-13} \\\Leftrightarrow &-11x & = &-25\\\Leftrightarrow & \color{red}{-11}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-25}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{25}{11} } & & \\ & V = \left\{ \frac{25}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{+6}& = & -1 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{+6}\color{blue}{-6+12x } & = & -1 \color{red}{ -12x }\color{blue}{-6+12x } \\\Leftrightarrow & 5x \color{blue}{+12x } & = & -1 \color{blue}{-6} \\\Leftrightarrow &17x & = &-7\\\Leftrightarrow & \color{red}{17}x & = &-7\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-7}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{17} } & & \\ & V = \left\{ \frac{-7}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{+4}& = & -8 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{+4}\color{blue}{-4+14x } & = & -8 \color{red}{ -14x }\color{blue}{-4+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & -8 \color{blue}{-4} \\\Leftrightarrow &29x & = &-12\\\Leftrightarrow & \color{red}{29}x & = &-12\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{-12}{29} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{29} } & & \\ & V = \left\{ \frac{-12}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{-14}& = & 11 \color{red}{ -7x } \\\Leftrightarrow & 11x \color{red}{-14}\color{blue}{+14+7x } & = & 11 \color{red}{ -7x }\color{blue}{+14+7x } \\\Leftrightarrow & 11x \color{blue}{+7x } & = & 11 \color{blue}{+14} \\\Leftrightarrow &18x & = &25\\\Leftrightarrow & \color{red}{18}x & = &25\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}} & = & \frac{25}{18} \\\Leftrightarrow & \color{green}{ x = \frac{25}{18} } & & \\ & V = \left\{ \frac{25}{18} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{+4}& = & 12 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{+4}\color{blue}{-4+8x } & = & 12 \color{red}{ -8x }\color{blue}{-4+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & 12 \color{blue}{-4} \\\Leftrightarrow &11x & = &8\\\Leftrightarrow & \color{red}{11}x & = &8\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{8}{11} \\\Leftrightarrow & \color{green}{ x = \frac{8}{11} } & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{-2}& = & -7 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{-2}\color{blue}{+2+2x } & = & -7 \color{red}{ -2x }\color{blue}{+2+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & -7 \color{blue}{+2} \\\Leftrightarrow &13x & = &-5\\\Leftrightarrow & \color{red}{13}x & = &-5\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-5}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{-7}& = & 10 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{-7}\color{blue}{+7-11x } & = & 10 \color{red}{ +11x }\color{blue}{+7-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & 10 \color{blue}{+7} \\\Leftrightarrow &-18x & = &17\\\Leftrightarrow & \color{red}{-18}x & = &17\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{17}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{18} } & & \\ & V = \left\{ \frac{-17}{18} \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{+13}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+13}\color{blue}{-13-x } & = & -14 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -14 \color{blue}{-13} \\\Leftrightarrow &-15x & = &-27\\\Leftrightarrow & \color{red}{-15}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-27}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{+15}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{+15}\color{blue}{-15-x } & = & -6 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & -6 \color{blue}{-15} \\\Leftrightarrow &3x & = &-21\\\Leftrightarrow & \color{red}{3}x & = &-21\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-21}{3} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{+12}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+12}\color{blue}{-12-x } & = & 7 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 7 \color{blue}{-12} \\\Leftrightarrow &-9x & = &-5\\\Leftrightarrow & \color{red}{-9}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-5}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{9} } & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{-9}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-9}\color{blue}{+9-x } & = & -7 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -7 \color{blue}{+9} \\\Leftrightarrow &-9x & = &2\\\Leftrightarrow & \color{red}{-9}x & = &2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)