Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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