Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{+9}& = & -9 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{+9}\color{blue}{-9-7x } & = & -9 \color{red}{ +7x }\color{blue}{-9-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & -9 \color{blue}{-9} \\\Leftrightarrow &-16x & = &-18\\\Leftrightarrow & \color{red}{-16}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-18}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{9}{8} } & & \\ & V = \left\{ \frac{9}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{+8}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+8}\color{blue}{-8-x } & = & 8 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 8 \color{blue}{-8} \\\Leftrightarrow &-4x & = &0\\\Leftrightarrow & \color{red}{-4}x & = &0\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{0}{-4} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{+12}& = & 5 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{+12}\color{blue}{-12-11x } & = & 5 \color{red}{ +11x }\color{blue}{-12-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & 5 \color{blue}{-12} \\\Leftrightarrow &-18x & = &-7\\\Leftrightarrow & \color{red}{-18}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{-7}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{7}{18} } & & \\ & V = \left\{ \frac{7}{18} \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{-7}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-7}\color{blue}{+7-x } & = & 13 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 13 \color{blue}{+7} \\\Leftrightarrow &-8x & = &20\\\Leftrightarrow & \color{red}{-8}x & = &20\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{20}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{+3}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+3}\color{blue}{-3-x } & = & 9 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 9 \color{blue}{-3} \\\Leftrightarrow &5x & = &6\\\Leftrightarrow & \color{red}{5}x & = &6\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{6}{5} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{+4}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+4}\color{blue}{-4-x } & = & -8 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -8 \color{blue}{-4} \\\Leftrightarrow &13x & = &-12\\\Leftrightarrow & \color{red}{13}x & = &-12\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-12}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{+14}& = & -5 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+14}\color{blue}{-14-x } & = & -5 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -5 \color{blue}{-14} \\\Leftrightarrow &13x & = &-19\\\Leftrightarrow & \color{red}{13}x & = &-19\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-19}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{13} } & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{-7}& = & -9 \color{red}{ -9x } \\\Leftrightarrow & 14x \color{red}{-7}\color{blue}{+7+9x } & = & -9 \color{red}{ -9x }\color{blue}{+7+9x } \\\Leftrightarrow & 14x \color{blue}{+9x } & = & -9 \color{blue}{+7} \\\Leftrightarrow &23x & = &-2\\\Leftrightarrow & \color{red}{23}x & = &-2\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-2}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{23} } & & \\ & V = \left\{ \frac{-2}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{-5}& = & 15 \color{red}{ -7x } \\\Leftrightarrow & x \color{red}{-5}\color{blue}{+5+7x } & = & 15 \color{red}{ -7x }\color{blue}{+5+7x } \\\Leftrightarrow & x \color{blue}{+7x } & = & 15 \color{blue}{+5} \\\Leftrightarrow &8x & = &20\\\Leftrightarrow & \color{red}{8}x & = &20\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{20}{8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{+14}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+14}\color{blue}{-14-x } & = & -8 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -8 \color{blue}{-14} \\\Leftrightarrow &-11x & = &-22\\\Leftrightarrow & \color{red}{-11}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-22}{-11} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{+12}& = & 3 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{+12}\color{blue}{-12-8x } & = & 3 \color{red}{ +8x }\color{blue}{-12-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & 3 \color{blue}{-12} \\\Leftrightarrow &-15x & = &-9\\\Leftrightarrow & \color{red}{-15}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-9}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{-10}& = & 11 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{-10}\color{blue}{+10+5x } & = & 11 \color{red}{ -5x }\color{blue}{+10+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 11 \color{blue}{+10} \\\Leftrightarrow &11x & = &21\\\Leftrightarrow & \color{red}{11}x & = &21\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{21}{11} \\\Leftrightarrow & \color{green}{ x = \frac{21}{11} } & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)