Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{+13}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+13}\color{blue}{-13-x } & = & -11 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -11 \color{blue}{-13} \\\Leftrightarrow &-6x & = &-24\\\Leftrightarrow & \color{red}{-6}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-24}{-6} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{+10}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+10}\color{blue}{-10-x } & = & -8 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -8 \color{blue}{-10} \\\Leftrightarrow &11x & = &-18\\\Leftrightarrow & \color{red}{11}x & = &-18\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-18}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{11} } & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{+11}& = & 14 \color{red}{ +7x } \\\Leftrightarrow & -2x \color{red}{+11}\color{blue}{-11-7x } & = & 14 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & -2x \color{blue}{-7x } & = & 14 \color{blue}{-11} \\\Leftrightarrow &-9x & = &3\\\Leftrightarrow & \color{red}{-9}x & = &3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{+13}& = & -11 \color{red}{ +3x } \\\Leftrightarrow & -14x \color{red}{+13}\color{blue}{-13-3x } & = & -11 \color{red}{ +3x }\color{blue}{-13-3x } \\\Leftrightarrow & -14x \color{blue}{-3x } & = & -11 \color{blue}{-13} \\\Leftrightarrow &-17x & = &-24\\\Leftrightarrow & \color{red}{-17}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-24}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{24}{17} } & & \\ & V = \left\{ \frac{24}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{-15}& = & 13 \color{red}{ +7x } \\\Leftrightarrow & 11x \color{red}{-15}\color{blue}{+15-7x } & = & 13 \color{red}{ +7x }\color{blue}{+15-7x } \\\Leftrightarrow & 11x \color{blue}{-7x } & = & 13 \color{blue}{+15} \\\Leftrightarrow &4x & = &28\\\Leftrightarrow & \color{red}{4}x & = &28\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{28}{4} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{+8}& = & 9 \color{red}{ +11x } \\\Leftrightarrow & x \color{red}{+8}\color{blue}{-8-11x } & = & 9 \color{red}{ +11x }\color{blue}{-8-11x } \\\Leftrightarrow & x \color{blue}{-11x } & = & 9 \color{blue}{-8} \\\Leftrightarrow &-10x & = &1\\\Leftrightarrow & \color{red}{-10}x & = &1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{+14}& = & -3 \color{red}{ +4x } \\\Leftrightarrow & -x \color{red}{+14}\color{blue}{-14-4x } & = & -3 \color{red}{ +4x }\color{blue}{-14-4x } \\\Leftrightarrow & -x \color{blue}{-4x } & = & -3 \color{blue}{-14} \\\Leftrightarrow &-5x & = &-17\\\Leftrightarrow & \color{red}{-5}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-17}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{17}{5} } & & \\ & V = \left\{ \frac{17}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{-5}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-5}\color{blue}{+5-x } & = & -1 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -1 \color{blue}{+5} \\\Leftrightarrow &-13x & = &4\\\Leftrightarrow & \color{red}{-13}x & = &4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{+6}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+6}\color{blue}{-6-x } & = & 1 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 1 \color{blue}{-6} \\\Leftrightarrow &-11x & = &-5\\\Leftrightarrow & \color{red}{-11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{-5}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-5}\color{blue}{+5-x } & = & -4 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -4 \color{blue}{+5} \\\Leftrightarrow &x & = &1\\\Leftrightarrow & \color{red}{}x & = &1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 1 \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{+9}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+9}\color{blue}{-9-x } & = & 9 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 9 \color{blue}{-9} \\\Leftrightarrow &-12x & = &0\\\Leftrightarrow & \color{red}{-12}x & = &0\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{0}{-12} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{+4}& = & -15 \color{red}{ +5x } \\\Leftrightarrow & -14x \color{red}{+4}\color{blue}{-4-5x } & = & -15 \color{red}{ +5x }\color{blue}{-4-5x } \\\Leftrightarrow & -14x \color{blue}{-5x } & = & -15 \color{blue}{-4} \\\Leftrightarrow &-19x & = &-19\\\Leftrightarrow & \color{red}{-19}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-19}{-19} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)