Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{-13}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-13}\color{blue}{+13-x } & = & 12 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 12 \color{blue}{+13} \\\Leftrightarrow &-9x & = &25\\\Leftrightarrow & \color{red}{-9}x & = &25\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{25}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{9} } & & \\ & V = \left\{ \frac{-25}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{+12}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{+12}\color{blue}{-12-7x } & = & -7 \color{red}{ +7x }\color{blue}{-12-7x } \\\Leftrightarrow & -3x \color{blue}{-7x } & = & -7 \color{blue}{-12} \\\Leftrightarrow &-10x & = &-19\\\Leftrightarrow & \color{red}{-10}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-19}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{19}{10} } & & \\ & V = \left\{ \frac{19}{10} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{+5}& = & 4 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+5}\color{blue}{-5-7x } & = & 4 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 4 \color{blue}{-5} \\\Leftrightarrow &-20x & = &-1\\\Leftrightarrow & \color{red}{-20}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-1}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{1}{20} } & & \\ & V = \left\{ \frac{1}{20} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{-7}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-7}\color{blue}{+7-x } & = & 3 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 3 \color{blue}{+7} \\\Leftrightarrow &-7x & = &10\\\Leftrightarrow & \color{red}{-7}x & = &10\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{10}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{7} } & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{-1}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-1}\color{blue}{+1-x } & = & 10 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 10 \color{blue}{+1} \\\Leftrightarrow &-7x & = &11\\\Leftrightarrow & \color{red}{-7}x & = &11\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{11}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{7} } & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{-13}& = & 5 \color{red}{ +7x } \\\Leftrightarrow & 6x \color{red}{-13}\color{blue}{+13-7x } & = & 5 \color{red}{ +7x }\color{blue}{+13-7x } \\\Leftrightarrow & 6x \color{blue}{-7x } & = & 5 \color{blue}{+13} \\\Leftrightarrow &-x & = &18\\\Leftrightarrow & \color{red}{-}x & = &18\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{18}{-1} \\\Leftrightarrow & \color{green}{ x = -18 } & & \\ & V = \left\{ -18 \right\} & \\\end{align}\)
7. \(\begin{align} & 6x \color{red}{-1}& = & -5 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-1}\color{blue}{+1+11x } & = & -5 \color{red}{ -11x }\color{blue}{+1+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -5 \color{blue}{+1} \\\Leftrightarrow &17x & = &-4\\\Leftrightarrow & \color{red}{17}x & = &-4\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-4}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{17} } & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{-5}& = & 14 \color{red}{ +5x } \\\Leftrightarrow & -14x \color{red}{-5}\color{blue}{+5-5x } & = & 14 \color{red}{ +5x }\color{blue}{+5-5x } \\\Leftrightarrow & -14x \color{blue}{-5x } & = & 14 \color{blue}{+5} \\\Leftrightarrow &-19x & = &19\\\Leftrightarrow & \color{red}{-19}x & = &19\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{19}{-19} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{+14}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+14}\color{blue}{-14-x } & = & 1 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 1 \color{blue}{-14} \\\Leftrightarrow &-11x & = &-13\\\Leftrightarrow & \color{red}{-11}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-13}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{13}{11} } & & \\ & V = \left\{ \frac{13}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{+14}& = & 7 \color{red}{ -7x } \\\Leftrightarrow & 11x \color{red}{+14}\color{blue}{-14+7x } & = & 7 \color{red}{ -7x }\color{blue}{-14+7x } \\\Leftrightarrow & 11x \color{blue}{+7x } & = & 7 \color{blue}{-14} \\\Leftrightarrow &18x & = &-7\\\Leftrightarrow & \color{red}{18}x & = &-7\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}} & = & \frac{-7}{18} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{18} } & & \\ & V = \left\{ \frac{-7}{18} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{+8}& = & 14 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{+8}\color{blue}{-8-11x } & = & 14 \color{red}{ +11x }\color{blue}{-8-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & 14 \color{blue}{-8} \\\Leftrightarrow &-5x & = &6\\\Leftrightarrow & \color{red}{-5}x & = &6\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{6}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{+2}& = & 13 \color{red}{ +6x } \\\Leftrightarrow & 7x \color{red}{+2}\color{blue}{-2-6x } & = & 13 \color{red}{ +6x }\color{blue}{-2-6x } \\\Leftrightarrow & 7x \color{blue}{-6x } & = & 13 \color{blue}{-2} \\\Leftrightarrow &x & = &11\\\Leftrightarrow & \color{red}{}x & = &11\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 11 \\\Leftrightarrow & \color{green}{ x = 11 } & & \\ & V = \left\{ 11 \right\} & \\\end{align}\)