Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{+5}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+5}\color{blue}{-5-x } & = & 1 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 1 \color{blue}{-5} \\\Leftrightarrow &5x & = &-4\\\Leftrightarrow & \color{red}{5}x & = &-4\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-4}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{-5}& = & 8 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{-5}\color{blue}{+5+13x } & = & 8 \color{red}{ -13x }\color{blue}{+5+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & 8 \color{blue}{+5} \\\Leftrightarrow &24x & = &13\\\Leftrightarrow & \color{red}{24}x & = &13\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{13}{24} \\\Leftrightarrow & \color{green}{ x = \frac{13}{24} } & & \\ & V = \left\{ \frac{13}{24} \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{-5}& = & 5 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{-5}\color{blue}{+5-9x } & = & 5 \color{red}{ +9x }\color{blue}{+5-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & 5 \color{blue}{+5} \\\Leftrightarrow &-20x & = &10\\\Leftrightarrow & \color{red}{-20}x & = &10\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{10}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-4}& = & -15 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-4}\color{blue}{+4-13x } & = & -15 \color{red}{ +13x }\color{blue}{+4-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -15 \color{blue}{+4} \\\Leftrightarrow &-28x & = &-11\\\Leftrightarrow & \color{red}{-28}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-11}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{11}{28} } & & \\ & V = \left\{ \frac{11}{28} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{-9}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-9}\color{blue}{+9-x } & = & 15 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 15 \color{blue}{+9} \\\Leftrightarrow &-4x & = &24\\\Leftrightarrow & \color{red}{-4}x & = &24\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{24}{-4} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{+5}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+5}\color{blue}{-5-x } & = & -14 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -14 \color{blue}{-5} \\\Leftrightarrow &-9x & = &-19\\\Leftrightarrow & \color{red}{-9}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-19}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{19}{9} } & & \\ & V = \left\{ \frac{19}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{-12}& = & 5 \color{red}{ -6x } \\\Leftrightarrow & -x \color{red}{-12}\color{blue}{+12+6x } & = & 5 \color{red}{ -6x }\color{blue}{+12+6x } \\\Leftrightarrow & -x \color{blue}{+6x } & = & 5 \color{blue}{+12} \\\Leftrightarrow &5x & = &17\\\Leftrightarrow & \color{red}{5}x & = &17\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{17}{5} \\\Leftrightarrow & \color{green}{ x = \frac{17}{5} } & & \\ & V = \left\{ \frac{17}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{+11}& = & -4 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{+11}\color{blue}{-11-10x } & = & -4 \color{red}{ +10x }\color{blue}{-11-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & -4 \color{blue}{-11} \\\Leftrightarrow &-19x & = &-15\\\Leftrightarrow & \color{red}{-19}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-15}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{15}{19} } & & \\ & V = \left\{ \frac{15}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{-11}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-11}\color{blue}{+11-x } & = & 4 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & 4 \color{blue}{+11} \\\Leftrightarrow &9x & = &15\\\Leftrightarrow & \color{red}{9}x & = &15\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{15}{9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{+10}& = & 3 \color{red}{ +11x } \\\Leftrightarrow & -2x \color{red}{+10}\color{blue}{-10-11x } & = & 3 \color{red}{ +11x }\color{blue}{-10-11x } \\\Leftrightarrow & -2x \color{blue}{-11x } & = & 3 \color{blue}{-10} \\\Leftrightarrow &-13x & = &-7\\\Leftrightarrow & \color{red}{-13}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{-10}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-10}\color{blue}{+10-x } & = & 3 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 3 \color{blue}{+10} \\\Leftrightarrow &-15x & = &13\\\Leftrightarrow & \color{red}{-15}x & = &13\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{13}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{15} } & & \\ & V = \left\{ \frac{-13}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{+10}& = & 4 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{+10}\color{blue}{-10-4x } & = & 4 \color{red}{ +4x }\color{blue}{-10-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & 4 \color{blue}{-10} \\\Leftrightarrow &-19x & = &-6\\\Leftrightarrow & \color{red}{-19}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-6}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{6}{19} } & & \\ & V = \left\{ \frac{6}{19} \right\} & \\\end{align}\)