Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{-3}& = & -12 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{-3}\color{blue}{+3-5x } & = & -12 \color{red}{ +5x }\color{blue}{+3-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & -12 \color{blue}{+3} \\\Leftrightarrow &-14x & = &-9\\\Leftrightarrow & \color{red}{-14}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-9}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{9}{14} } & & \\ & V = \left\{ \frac{9}{14} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{-1}& = & 6 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-1}\color{blue}{+1+11x } & = & 6 \color{red}{ -11x }\color{blue}{+1+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 6 \color{blue}{+1} \\\Leftrightarrow &17x & = &7\\\Leftrightarrow & \color{red}{17}x & = &7\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{7}{17} \\\Leftrightarrow & \color{green}{ x = \frac{7}{17} } & & \\ & V = \left\{ \frac{7}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{+7}& = & -14 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{+7}\color{blue}{-7-11x } & = & -14 \color{red}{ +11x }\color{blue}{-7-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & -14 \color{blue}{-7} \\\Leftrightarrow &-5x & = &-21\\\Leftrightarrow & \color{red}{-5}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-21}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{21}{5} } & & \\ & V = \left\{ \frac{21}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{+8}& = & -8 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+8}\color{blue}{-8+11x } & = & -8 \color{red}{ -11x }\color{blue}{-8+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -8 \color{blue}{-8} \\\Leftrightarrow &17x & = &-16\\\Leftrightarrow & \color{red}{17}x & = &-16\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-16}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{17} } & & \\ & V = \left\{ \frac{-16}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{-3}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-3}\color{blue}{+3-x } & = & 12 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 12 \color{blue}{+3} \\\Leftrightarrow &-6x & = &15\\\Leftrightarrow & \color{red}{-6}x & = &15\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{15}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{-6}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-6}\color{blue}{+6-x } & = & -12 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -12 \color{blue}{+6} \\\Leftrightarrow &-9x & = &-6\\\Leftrightarrow & \color{red}{-9}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{+6}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+6}\color{blue}{-6-x } & = & 15 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 15 \color{blue}{-6} \\\Leftrightarrow &-14x & = &9\\\Leftrightarrow & \color{red}{-14}x & = &9\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{9}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{14} } & & \\ & V = \left\{ \frac{-9}{14} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{+13}& = & -5 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{+13}\color{blue}{-13-x } & = & -5 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & -5 \color{blue}{-13} \\\Leftrightarrow &2x & = &-18\\\Leftrightarrow & \color{red}{2}x & = &-18\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-18}{2} \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{-9}& = & 15 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{-9}\color{blue}{+9+7x } & = & 15 \color{red}{ -7x }\color{blue}{+9+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & 15 \color{blue}{+9} \\\Leftrightarrow &22x & = &24\\\Leftrightarrow & \color{red}{22}x & = &24\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{24}{22} \\\Leftrightarrow & \color{green}{ x = \frac{12}{11} } & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{+14}& = & -4 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{+14}\color{blue}{-14-6x } & = & -4 \color{red}{ +6x }\color{blue}{-14-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & -4 \color{blue}{-14} \\\Leftrightarrow &-11x & = &-18\\\Leftrightarrow & \color{red}{-11}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-18}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{18}{11} } & & \\ & V = \left\{ \frac{18}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{+5}& = & 13 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{+5}\color{blue}{-5+9x } & = & 13 \color{red}{ -9x }\color{blue}{-5+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & 13 \color{blue}{-5} \\\Leftrightarrow &19x & = &8\\\Leftrightarrow & \color{red}{19}x & = &8\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{8}{19} \\\Leftrightarrow & \color{green}{ x = \frac{8}{19} } & & \\ & V = \left\{ \frac{8}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{+7}& = & -4 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{+7}\color{blue}{-7+3x } & = & -4 \color{red}{ -3x }\color{blue}{-7+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & -4 \color{blue}{-7} \\\Leftrightarrow &10x & = &-11\\\Leftrightarrow & \color{red}{10}x & = &-11\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-11}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{10} } & & \\ & V = \left\{ \frac{-11}{10} \right\} & \\\end{align}\)