Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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