Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{-13}& = & 9 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{-13}\color{blue}{+13-9x } & = & 9 \color{red}{ +9x }\color{blue}{+13-9x } \\\Leftrightarrow & 4x \color{blue}{-9x } & = & 9 \color{blue}{+13} \\\Leftrightarrow &-5x & = &22\\\Leftrightarrow & \color{red}{-5}x & = &22\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{22}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{5} } & & \\ & V = \left\{ \frac{-22}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{-15}& = & 15 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-15}\color{blue}{+15-7x } & = & 15 \color{red}{ +7x }\color{blue}{+15-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & 15 \color{blue}{+15} \\\Leftrightarrow &-13x & = &30\\\Leftrightarrow & \color{red}{-13}x & = &30\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{30}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-30}{13} } & & \\ & V = \left\{ \frac{-30}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{-3}& = & 14 \color{red}{ -3x } \\\Leftrightarrow & x \color{red}{-3}\color{blue}{+3+3x } & = & 14 \color{red}{ -3x }\color{blue}{+3+3x } \\\Leftrightarrow & x \color{blue}{+3x } & = & 14 \color{blue}{+3} \\\Leftrightarrow &4x & = &17\\\Leftrightarrow & \color{red}{4}x & = &17\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{17}{4} \\\Leftrightarrow & \color{green}{ x = \frac{17}{4} } & & \\ & V = \left\{ \frac{17}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{+6}& = & 4 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+6}\color{blue}{-6+13x } & = & 4 \color{red}{ -13x }\color{blue}{-6+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & 4 \color{blue}{-6} \\\Leftrightarrow &20x & = &-2\\\Leftrightarrow & \color{red}{20}x & = &-2\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-2}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{-13}& = & 7 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{-13}\color{blue}{+13+15x } & = & 7 \color{red}{ -15x }\color{blue}{+13+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & 7 \color{blue}{+13} \\\Leftrightarrow &23x & = &20\\\Leftrightarrow & \color{red}{23}x & = &20\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{20}{23} \\\Leftrightarrow & \color{green}{ x = \frac{20}{23} } & & \\ & V = \left\{ \frac{20}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{+15}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+15}\color{blue}{-15-x } & = & -2 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -2 \color{blue}{-15} \\\Leftrightarrow &x & = &-17\\\Leftrightarrow & \color{red}{}x & = &-17\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -17 \\\Leftrightarrow & \color{green}{ x = -17 } & & \\ & V = \left\{ -17 \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{+10}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 15x \color{red}{+10}\color{blue}{-10-x } & = & -9 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & 15x \color{blue}{-x } & = & -9 \color{blue}{-10} \\\Leftrightarrow &14x & = &-19\\\Leftrightarrow & \color{red}{14}x & = &-19\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-19}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{14} } & & \\ & V = \left\{ \frac{-19}{14} \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{+2}& = & -8 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{+2}\color{blue}{-2+14x } & = & -8 \color{red}{ -14x }\color{blue}{-2+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & -8 \color{blue}{-2} \\\Leftrightarrow &29x & = &-10\\\Leftrightarrow & \color{red}{29}x & = &-10\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{-10}{29} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{29} } & & \\ & V = \left\{ \frac{-10}{29} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{+14}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+14}\color{blue}{-14-x } & = & -11 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -11 \color{blue}{-14} \\\Leftrightarrow &-9x & = &-25\\\Leftrightarrow & \color{red}{-9}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-25}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{25}{9} } & & \\ & V = \left\{ \frac{25}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{-11}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-11}\color{blue}{+11-x } & = & -10 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -10 \color{blue}{+11} \\\Leftrightarrow &x & = &1\\\Leftrightarrow & \color{red}{}x & = &1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 1 \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{+12}& = & -3 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{+12}\color{blue}{-12+10x } & = & -3 \color{red}{ -10x }\color{blue}{-12+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & -3 \color{blue}{-12} \\\Leftrightarrow &21x & = &-15\\\Leftrightarrow & \color{red}{21}x & = &-15\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-15}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{+8}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+8}\color{blue}{-8-x } & = & 10 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 10 \color{blue}{-8} \\\Leftrightarrow &-15x & = &2\\\Leftrightarrow & \color{red}{-15}x & = &2\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{2}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{15} } & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)