Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{-13}& = & -14 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{-13}\color{blue}{+13-10x } & = & -14 \color{red}{ +10x }\color{blue}{+13-10x } \\\Leftrightarrow & 9x \color{blue}{-10x } & = & -14 \color{blue}{+13} \\\Leftrightarrow &-x & = &-1\\\Leftrightarrow & \color{red}{-}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-1}{-1} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{+10}& = & -8 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{+10}\color{blue}{-10-10x } & = & -8 \color{red}{ +10x }\color{blue}{-10-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & -8 \color{blue}{-10} \\\Leftrightarrow &-13x & = &-18\\\Leftrightarrow & \color{red}{-13}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-18}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{18}{13} } & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{-15}& = & -5 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{-15}\color{blue}{+15-5x } & = & -5 \color{red}{ +5x }\color{blue}{+15-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & -5 \color{blue}{+15} \\\Leftrightarrow &-9x & = &10\\\Leftrightarrow & \color{red}{-9}x & = &10\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{10}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{9} } & & \\ & V = \left\{ \frac{-10}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{-3}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-3}\color{blue}{+3-x } & = & -11 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -11 \color{blue}{+3} \\\Leftrightarrow &-13x & = &-8\\\Leftrightarrow & \color{red}{-13}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-8}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{8}{13} } & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{+4}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+4}\color{blue}{-4-x } & = & -2 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -2 \color{blue}{-4} \\\Leftrightarrow &-13x & = &-6\\\Leftrightarrow & \color{red}{-13}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{6}{13} } & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{+4}& = & 15 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{+4}\color{blue}{-4-9x } & = & 15 \color{red}{ +9x }\color{blue}{-4-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & 15 \color{blue}{-4} \\\Leftrightarrow &-13x & = &11\\\Leftrightarrow & \color{red}{-13}x & = &11\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{11}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{13} } & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{-14}& = & 8 \color{red}{ +2x } \\\Leftrightarrow & 7x \color{red}{-14}\color{blue}{+14-2x } & = & 8 \color{red}{ +2x }\color{blue}{+14-2x } \\\Leftrightarrow & 7x \color{blue}{-2x } & = & 8 \color{blue}{+14} \\\Leftrightarrow &5x & = &22\\\Leftrightarrow & \color{red}{5}x & = &22\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{22}{5} \\\Leftrightarrow & \color{green}{ x = \frac{22}{5} } & & \\ & V = \left\{ \frac{22}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{-12}& = & -14 \color{red}{ +3x } \\\Leftrightarrow & 14x \color{red}{-12}\color{blue}{+12-3x } & = & -14 \color{red}{ +3x }\color{blue}{+12-3x } \\\Leftrightarrow & 14x \color{blue}{-3x } & = & -14 \color{blue}{+12} \\\Leftrightarrow &11x & = &-2\\\Leftrightarrow & \color{red}{11}x & = &-2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{+12}& = & 1 \color{red}{ +2x } \\\Leftrightarrow & 7x \color{red}{+12}\color{blue}{-12-2x } & = & 1 \color{red}{ +2x }\color{blue}{-12-2x } \\\Leftrightarrow & 7x \color{blue}{-2x } & = & 1 \color{blue}{-12} \\\Leftrightarrow &5x & = &-11\\\Leftrightarrow & \color{red}{5}x & = &-11\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-11}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{5} } & & \\ & V = \left\{ \frac{-11}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{+7}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+7}\color{blue}{-7-x } & = & -14 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -14 \color{blue}{-7} \\\Leftrightarrow &x & = &-21\\\Leftrightarrow & \color{red}{}x & = &-21\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -21 \\\Leftrightarrow & \color{green}{ x = -21 } & & \\ & V = \left\{ -21 \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{-12}& = & 3 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{-12}\color{blue}{+12+4x } & = & 3 \color{red}{ -4x }\color{blue}{+12+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & 3 \color{blue}{+12} \\\Leftrightarrow &13x & = &15\\\Leftrightarrow & \color{red}{13}x & = &15\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{15}{13} \\\Leftrightarrow & \color{green}{ x = \frac{15}{13} } & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{+15}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+15}\color{blue}{-15-x } & = & 11 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 11 \color{blue}{-15} \\\Leftrightarrow &-12x & = &-4\\\Leftrightarrow & \color{red}{-12}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-4}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)