Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{+3}& = & 3 \color{red}{ +3x } \\\Leftrightarrow & x \color{red}{+3}\color{blue}{-3-3x } & = & 3 \color{red}{ +3x }\color{blue}{-3-3x } \\\Leftrightarrow & x \color{blue}{-3x } & = & 3 \color{blue}{-3} \\\Leftrightarrow &-2x & = &0\\\Leftrightarrow & \color{red}{-2}x & = &0\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{0}{-2} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{-1}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-1}\color{blue}{+1-x } & = & 12 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 12 \color{blue}{+1} \\\Leftrightarrow &-13x & = &13\\\Leftrightarrow & \color{red}{-13}x & = &13\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{13}{-13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{+1}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+1}\color{blue}{-1-x } & = & 10 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 10 \color{blue}{-1} \\\Leftrightarrow &-9x & = &9\\\Leftrightarrow & \color{red}{-9}x & = &9\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{9}{-9} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{-8}& = & -2 \color{red}{ +8x } \\\Leftrightarrow & 13x \color{red}{-8}\color{blue}{+8-8x } & = & -2 \color{red}{ +8x }\color{blue}{+8-8x } \\\Leftrightarrow & 13x \color{blue}{-8x } & = & -2 \color{blue}{+8} \\\Leftrightarrow &5x & = &6\\\Leftrightarrow & \color{red}{5}x & = &6\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{6}{5} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{+12}& = & -15 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{+12}\color{blue}{-12-9x } & = & -15 \color{red}{ +9x }\color{blue}{-12-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & -15 \color{blue}{-12} \\\Leftrightarrow &5x & = &-27\\\Leftrightarrow & \color{red}{5}x & = &-27\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-27}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{5} } & & \\ & V = \left\{ \frac{-27}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{+12}& = & 10 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+12}\color{blue}{-12+13x } & = & 10 \color{red}{ -13x }\color{blue}{-12+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & 10 \color{blue}{-12} \\\Leftrightarrow &24x & = &-2\\\Leftrightarrow & \color{red}{24}x & = &-2\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-2}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{12} } & & \\ & V = \left\{ \frac{-1}{12} \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{+13}& = & 10 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{+13}\color{blue}{-13-5x } & = & 10 \color{red}{ +5x }\color{blue}{-13-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & 10 \color{blue}{-13} \\\Leftrightarrow &-17x & = &-3\\\Leftrightarrow & \color{red}{-17}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-3}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{3}{17} } & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{-14}& = & 14 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{-14}\color{blue}{+14+13x } & = & 14 \color{red}{ -13x }\color{blue}{+14+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & 14 \color{blue}{+14} \\\Leftrightarrow &20x & = &28\\\Leftrightarrow & \color{red}{20}x & = &28\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{28}{20} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{-15}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{-15}\color{blue}{+15-7x } & = & 11 \color{red}{ +7x }\color{blue}{+15-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & 11 \color{blue}{+15} \\\Leftrightarrow &8x & = &26\\\Leftrightarrow & \color{red}{8}x & = &26\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{26}{8} \\\Leftrightarrow & \color{green}{ x = \frac{13}{4} } & & \\ & V = \left\{ \frac{13}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{-12}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-12}\color{blue}{+12-x } & = & 1 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & 1 \color{blue}{+12} \\\Leftrightarrow &9x & = &13\\\Leftrightarrow & \color{red}{9}x & = &13\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{13}{9} \\\Leftrightarrow & \color{green}{ x = \frac{13}{9} } & & \\ & V = \left\{ \frac{13}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{+9}& = & 4 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+9}\color{blue}{-9+3x } & = & 4 \color{red}{ -3x }\color{blue}{-9+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 4 \color{blue}{-9} \\\Leftrightarrow &13x & = &-5\\\Leftrightarrow & \color{red}{13}x & = &-5\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-5}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{+9}& = & 2 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{+9}\color{blue}{-9-9x } & = & 2 \color{red}{ +9x }\color{blue}{-9-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & 2 \color{blue}{-9} \\\Leftrightarrow &5x & = &-7\\\Leftrightarrow & \color{red}{5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-7}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)