Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{+5}& = & -1 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+5}\color{blue}{-5-5x } & = & -1 \color{red}{ +5x }\color{blue}{-5-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -1 \color{blue}{-5} \\\Leftrightarrow &7x & = &-6\\\Leftrightarrow & \color{red}{7}x & = &-6\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-6}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{+2}& = & 4 \color{red}{ -6x } \\\Leftrightarrow & -x \color{red}{+2}\color{blue}{-2+6x } & = & 4 \color{red}{ -6x }\color{blue}{-2+6x } \\\Leftrightarrow & -x \color{blue}{+6x } & = & 4 \color{blue}{-2} \\\Leftrightarrow &5x & = &2\\\Leftrightarrow & \color{red}{5}x & = &2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{+9}& = & -13 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+9}\color{blue}{-9-13x } & = & -13 \color{red}{ +13x }\color{blue}{-9-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -13 \color{blue}{-9} \\\Leftrightarrow &-28x & = &-22\\\Leftrightarrow & \color{red}{-28}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-22}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{11}{14} } & & \\ & V = \left\{ \frac{11}{14} \right\} & \\\end{align}\)
4. \(\begin{align} & x \color{red}{-14}& = & -9 \color{red}{ +9x } \\\Leftrightarrow & x \color{red}{-14}\color{blue}{+14-9x } & = & -9 \color{red}{ +9x }\color{blue}{+14-9x } \\\Leftrightarrow & x \color{blue}{-9x } & = & -9 \color{blue}{+14} \\\Leftrightarrow &-8x & = &5\\\Leftrightarrow & \color{red}{-8}x & = &5\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{5}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & -10x \color{red}{+5}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+5}\color{blue}{-5-x } & = & -8 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -8 \color{blue}{-5} \\\Leftrightarrow &-11x & = &-13\\\Leftrightarrow & \color{red}{-11}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-13}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{13}{11} } & & \\ & V = \left\{ \frac{13}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{+1}& = & -3 \color{red}{ +13x } \\\Leftrightarrow & 9x \color{red}{+1}\color{blue}{-1-13x } & = & -3 \color{red}{ +13x }\color{blue}{-1-13x } \\\Leftrightarrow & 9x \color{blue}{-13x } & = & -3 \color{blue}{-1} \\\Leftrightarrow &-4x & = &-4\\\Leftrightarrow & \color{red}{-4}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-4}{-4} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{-13}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-13}\color{blue}{+13-x } & = & 13 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 13 \color{blue}{+13} \\\Leftrightarrow &-13x & = &26\\\Leftrightarrow & \color{red}{-13}x & = &26\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{26}{-13} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{+6}& = & 15 \color{red}{ +11x } \\\Leftrightarrow & 9x \color{red}{+6}\color{blue}{-6-11x } & = & 15 \color{red}{ +11x }\color{blue}{-6-11x } \\\Leftrightarrow & 9x \color{blue}{-11x } & = & 15 \color{blue}{-6} \\\Leftrightarrow &-2x & = &9\\\Leftrightarrow & \color{red}{-2}x & = &9\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{9}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{2} } & & \\ & V = \left\{ \frac{-9}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{+13}& = & -4 \color{red}{ +5x } \\\Leftrightarrow & 3x \color{red}{+13}\color{blue}{-13-5x } & = & -4 \color{red}{ +5x }\color{blue}{-13-5x } \\\Leftrightarrow & 3x \color{blue}{-5x } & = & -4 \color{blue}{-13} \\\Leftrightarrow &-2x & = &-17\\\Leftrightarrow & \color{red}{-2}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-17}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{17}{2} } & & \\ & V = \left\{ \frac{17}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{+9}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+9}\color{blue}{-9-x } & = & 15 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 15 \color{blue}{-9} \\\Leftrightarrow &-12x & = &6\\\Leftrightarrow & \color{red}{-12}x & = &6\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{6}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{+8}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+8}\color{blue}{-8-x } & = & 3 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 3 \color{blue}{-8} \\\Leftrightarrow &-3x & = &-5\\\Leftrightarrow & \color{red}{-3}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-5}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{-8}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-8}\color{blue}{+8-x } & = & 10 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 10 \color{blue}{+8} \\\Leftrightarrow &11x & = &18\\\Leftrightarrow & \color{red}{11}x & = &18\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{18}{11} \\\Leftrightarrow & \color{green}{ x = \frac{18}{11} } & & \\ & V = \left\{ \frac{18}{11} \right\} & \\\end{align}\)