Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{-9}& = & 7 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{-9}\color{blue}{+9+12x } & = & 7 \color{red}{ -12x }\color{blue}{+9+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & 7 \color{blue}{+9} \\\Leftrightarrow &25x & = &16\\\Leftrightarrow & \color{red}{25}x & = &16\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{16}{25} \\\Leftrightarrow & \color{green}{ x = \frac{16}{25} } & & \\ & V = \left\{ \frac{16}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{+1}& = & 1 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+1}\color{blue}{-1+7x } & = & 1 \color{red}{ -7x }\color{blue}{-1+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 1 \color{blue}{-1} \\\Leftrightarrow &15x & = &0\\\Leftrightarrow & \color{red}{15}x & = &0\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{0}{15} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{-3}& = & 10 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-3}\color{blue}{+3+11x } & = & 10 \color{red}{ -11x }\color{blue}{+3+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 10 \color{blue}{+3} \\\Leftrightarrow &23x & = &13\\\Leftrightarrow & \color{red}{23}x & = &13\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{13}{23} \\\Leftrightarrow & \color{green}{ x = \frac{13}{23} } & & \\ & V = \left\{ \frac{13}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{-14}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-14}\color{blue}{+14-x } & = & -11 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -11 \color{blue}{+14} \\\Leftrightarrow &-13x & = &3\\\Leftrightarrow & \color{red}{-13}x & = &3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{-12}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-12}\color{blue}{+12-x } & = & -2 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -2 \color{blue}{+12} \\\Leftrightarrow &-9x & = &10\\\Leftrightarrow & \color{red}{-9}x & = &10\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{10}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{9} } & & \\ & V = \left\{ \frac{-10}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{-13}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-13}\color{blue}{+13-x } & = & -2 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -2 \color{blue}{+13} \\\Leftrightarrow &-9x & = &11\\\Leftrightarrow & \color{red}{-9}x & = &11\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{11}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{9} } & & \\ & V = \left\{ \frac{-11}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{-13}& = & 9 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{-13}\color{blue}{+13+2x } & = & 9 \color{red}{ -2x }\color{blue}{+13+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & 9 \color{blue}{+13} \\\Leftrightarrow &13x & = &22\\\Leftrightarrow & \color{red}{13}x & = &22\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{22}{13} \\\Leftrightarrow & \color{green}{ x = \frac{22}{13} } & & \\ & V = \left\{ \frac{22}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{-3}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-3}\color{blue}{+3-x } & = & 7 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 7 \color{blue}{+3} \\\Leftrightarrow &-4x & = &10\\\Leftrightarrow & \color{red}{-4}x & = &10\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{10}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{-13}& = & 8 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-13}\color{blue}{+13-9x } & = & 8 \color{red}{ +9x }\color{blue}{+13-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 8 \color{blue}{+13} \\\Leftrightarrow &-17x & = &21\\\Leftrightarrow & \color{red}{-17}x & = &21\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{21}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{17} } & & \\ & V = \left\{ \frac{-21}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{+5}& = & 15 \color{red}{ +10x } \\\Leftrightarrow & -13x \color{red}{+5}\color{blue}{-5-10x } & = & 15 \color{red}{ +10x }\color{blue}{-5-10x } \\\Leftrightarrow & -13x \color{blue}{-10x } & = & 15 \color{blue}{-5} \\\Leftrightarrow &-23x & = &10\\\Leftrightarrow & \color{red}{-23}x & = &10\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{10}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{23} } & & \\ & V = \left\{ \frac{-10}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{-3}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-3}\color{blue}{+3-x } & = & -11 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & -11 \color{blue}{+3} \\\Leftrightarrow &9x & = &-8\\\Leftrightarrow & \color{red}{9}x & = &-8\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-8}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{9} } & & \\ & V = \left\{ \frac{-8}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{-14}& = & -7 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{-14}\color{blue}{+14+7x } & = & -7 \color{red}{ -7x }\color{blue}{+14+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & -7 \color{blue}{+14} \\\Leftrightarrow &11x & = &7\\\Leftrightarrow & \color{red}{11}x & = &7\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{7}{11} \\\Leftrightarrow & \color{green}{ x = \frac{7}{11} } & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)