Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{-10}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-10}\color{blue}{+10-x } & = & -13 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -13 \color{blue}{+10} \\\Leftrightarrow &-5x & = &-3\\\Leftrightarrow & \color{red}{-5}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{-8}& = & 1 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-8}\color{blue}{+8-9x } & = & 1 \color{red}{ +9x }\color{blue}{+8-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 1 \color{blue}{+8} \\\Leftrightarrow &-17x & = &9\\\Leftrightarrow & \color{red}{-17}x & = &9\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{9}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{17} } & & \\ & V = \left\{ \frac{-9}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{-3}& = & -13 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-3}\color{blue}{+3-7x } & = & -13 \color{red}{ +7x }\color{blue}{+3-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -13 \color{blue}{+3} \\\Leftrightarrow &-13x & = &-10\\\Leftrightarrow & \color{red}{-13}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{-12}& = & 14 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{-12}\color{blue}{+12+14x } & = & 14 \color{red}{ -14x }\color{blue}{+12+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & 14 \color{blue}{+12} \\\Leftrightarrow &19x & = &26\\\Leftrightarrow & \color{red}{19}x & = &26\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{26}{19} \\\Leftrightarrow & \color{green}{ x = \frac{26}{19} } & & \\ & V = \left\{ \frac{26}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{-10}& = & 9 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{-10}\color{blue}{+10-11x } & = & 9 \color{red}{ +11x }\color{blue}{+10-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & 9 \color{blue}{+10} \\\Leftrightarrow &-5x & = &19\\\Leftrightarrow & \color{red}{-5}x & = &19\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{19}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{5} } & & \\ & V = \left\{ \frac{-19}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{+15}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+15}\color{blue}{-15-x } & = & 8 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 8 \color{blue}{-15} \\\Leftrightarrow &-12x & = &-7\\\Leftrightarrow & \color{red}{-12}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-7}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{12} } & & \\ & V = \left\{ \frac{7}{12} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{+10}& = & -9 \color{red}{ +10x } \\\Leftrightarrow & -x \color{red}{+10}\color{blue}{-10-10x } & = & -9 \color{red}{ +10x }\color{blue}{-10-10x } \\\Leftrightarrow & -x \color{blue}{-10x } & = & -9 \color{blue}{-10} \\\Leftrightarrow &-11x & = &-19\\\Leftrightarrow & \color{red}{-11}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-19}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{19}{11} } & & \\ & V = \left\{ \frac{19}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{-6}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-6}\color{blue}{+6-x } & = & 11 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 11 \color{blue}{+6} \\\Leftrightarrow &-16x & = &17\\\Leftrightarrow & \color{red}{-16}x & = &17\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{17}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{16} } & & \\ & V = \left\{ \frac{-17}{16} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{+3}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+3}\color{blue}{-3-x } & = & 12 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 12 \color{blue}{-3} \\\Leftrightarrow &-5x & = &9\\\Leftrightarrow & \color{red}{-5}x & = &9\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{9}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{+9}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+9}\color{blue}{-9-x } & = & 7 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 7 \color{blue}{-9} \\\Leftrightarrow &-5x & = &-2\\\Leftrightarrow & \color{red}{-5}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{+15}& = & -10 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+15}\color{blue}{-15+13x } & = & -10 \color{red}{ -13x }\color{blue}{-15+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & -10 \color{blue}{-15} \\\Leftrightarrow &24x & = &-25\\\Leftrightarrow & \color{red}{24}x & = &-25\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-25}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{24} } & & \\ & V = \left\{ \frac{-25}{24} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{-4}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-4}\color{blue}{+4-x } & = & 10 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 10 \color{blue}{+4} \\\Leftrightarrow &-10x & = &14\\\Leftrightarrow & \color{red}{-10}x & = &14\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{14}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)