Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{+7}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+7}\color{blue}{-7-x } & = & 10 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 10 \color{blue}{-7} \\\Leftrightarrow &-10x & = &3\\\Leftrightarrow & \color{red}{-10}x & = &3\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{3}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{10} } & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{-12}& = & -2 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{-12}\color{blue}{+12-12x } & = & -2 \color{red}{ +12x }\color{blue}{+12-12x } \\\Leftrightarrow & 11x \color{blue}{-12x } & = & -2 \color{blue}{+12} \\\Leftrightarrow &-x & = &10\\\Leftrightarrow & \color{red}{-}x & = &10\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{10}{-1} \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{-11}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11-x } & = & 6 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 6 \color{blue}{+11} \\\Leftrightarrow &-6x & = &17\\\Leftrightarrow & \color{red}{-6}x & = &17\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{17}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{6} } & & \\ & V = \left\{ \frac{-17}{6} \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{-15}& = & 11 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{-15}\color{blue}{+15+11x } & = & 11 \color{red}{ -11x }\color{blue}{+15+11x } \\\Leftrightarrow & 9x \color{blue}{+11x } & = & 11 \color{blue}{+15} \\\Leftrightarrow &20x & = &26\\\Leftrightarrow & \color{red}{20}x & = &26\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{26}{20} \\\Leftrightarrow & \color{green}{ x = \frac{13}{10} } & & \\ & V = \left\{ \frac{13}{10} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{-5}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-5}\color{blue}{+5-x } & = & 5 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 5 \color{blue}{+5} \\\Leftrightarrow &-15x & = &10\\\Leftrightarrow & \color{red}{-15}x & = &10\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{10}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{-10}& = & 12 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{-10}\color{blue}{+10+11x } & = & 12 \color{red}{ -11x }\color{blue}{+10+11x } \\\Leftrightarrow & 9x \color{blue}{+11x } & = & 12 \color{blue}{+10} \\\Leftrightarrow &20x & = &22\\\Leftrightarrow & \color{red}{20}x & = &22\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{22}{20} \\\Leftrightarrow & \color{green}{ x = \frac{11}{10} } & & \\ & V = \left\{ \frac{11}{10} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{-8}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{-8}\color{blue}{+8-13x } & = & 11 \color{red}{ +13x }\color{blue}{+8-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & 11 \color{blue}{+8} \\\Leftrightarrow &-16x & = &19\\\Leftrightarrow & \color{red}{-16}x & = &19\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{19}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{16} } & & \\ & V = \left\{ \frac{-19}{16} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{-7}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-7}\color{blue}{+7-x } & = & -15 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -15 \color{blue}{+7} \\\Leftrightarrow &-9x & = &-8\\\Leftrightarrow & \color{red}{-9}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-8}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{8}{9} } & & \\ & V = \left\{ \frac{8}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{+3}& = & 15 \color{red}{ +4x } \\\Leftrightarrow & 15x \color{red}{+3}\color{blue}{-3-4x } & = & 15 \color{red}{ +4x }\color{blue}{-3-4x } \\\Leftrightarrow & 15x \color{blue}{-4x } & = & 15 \color{blue}{-3} \\\Leftrightarrow &11x & = &12\\\Leftrightarrow & \color{red}{11}x & = &12\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{12}{11} \\\Leftrightarrow & \color{green}{ x = \frac{12}{11} } & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{-7}& = & 7 \color{red}{ +7x } \\\Leftrightarrow & 5x \color{red}{-7}\color{blue}{+7-7x } & = & 7 \color{red}{ +7x }\color{blue}{+7-7x } \\\Leftrightarrow & 5x \color{blue}{-7x } & = & 7 \color{blue}{+7} \\\Leftrightarrow &-2x & = &14\\\Leftrightarrow & \color{red}{-2}x & = &14\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{14}{-2} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{+5}& = & -3 \color{red}{ +3x } \\\Leftrightarrow & -x \color{red}{+5}\color{blue}{-5-3x } & = & -3 \color{red}{ +3x }\color{blue}{-5-3x } \\\Leftrightarrow & -x \color{blue}{-3x } & = & -3 \color{blue}{-5} \\\Leftrightarrow &-4x & = &-8\\\Leftrightarrow & \color{red}{-4}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-8}{-4} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{+8}& = & -4 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+8}\color{blue}{-8+2x } & = & -4 \color{red}{ -2x }\color{blue}{-8+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -4 \color{blue}{-8} \\\Leftrightarrow &17x & = &-12\\\Leftrightarrow & \color{red}{17}x & = &-12\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-12}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{17} } & & \\ & V = \left\{ \frac{-12}{17} \right\} & \\\end{align}\)