Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{+13}& = & -14 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{+13}\color{blue}{-13-11x } & = & -14 \color{red}{ +11x }\color{blue}{-13-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & -14 \color{blue}{-13} \\\Leftrightarrow &4x & = &-27\\\Leftrightarrow & \color{red}{4}x & = &-27\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-27}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{4} } & & \\ & V = \left\{ \frac{-27}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{-15}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & 11x \color{red}{-15}\color{blue}{+15-13x } & = & 3 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & 11x \color{blue}{-13x } & = & 3 \color{blue}{+15} \\\Leftrightarrow &-2x & = &18\\\Leftrightarrow & \color{red}{-2}x & = &18\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{18}{-2} \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{+11}& = & 15 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+11}\color{blue}{-11+13x } & = & 15 \color{red}{ -13x }\color{blue}{-11+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & 15 \color{blue}{-11} \\\Leftrightarrow &20x & = &4\\\Leftrightarrow & \color{red}{20}x & = &4\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{4}{20} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{-9}& = & 11 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-9}\color{blue}{+9-x } & = & 11 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & 11 \color{blue}{+9} \\\Leftrightarrow &3x & = &20\\\Leftrightarrow & \color{red}{3}x & = &20\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{20}{3} \\\Leftrightarrow & \color{green}{ x = \frac{20}{3} } & & \\ & V = \left\{ \frac{20}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{+15}& = & 2 \color{red}{ +9x } \\\Leftrightarrow & -x \color{red}{+15}\color{blue}{-15-9x } & = & 2 \color{red}{ +9x }\color{blue}{-15-9x } \\\Leftrightarrow & -x \color{blue}{-9x } & = & 2 \color{blue}{-15} \\\Leftrightarrow &-10x & = &-13\\\Leftrightarrow & \color{red}{-10}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-13}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{13}{10} } & & \\ & V = \left\{ \frac{13}{10} \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{-5}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-5}\color{blue}{+5-x } & = & 2 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 2 \color{blue}{+5} \\\Leftrightarrow &-4x & = &7\\\Leftrightarrow & \color{red}{-4}x & = &7\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{7}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{-15}& = & 8 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{-15}\color{blue}{+15-12x } & = & 8 \color{red}{ +12x }\color{blue}{+15-12x } \\\Leftrightarrow & 11x \color{blue}{-12x } & = & 8 \color{blue}{+15} \\\Leftrightarrow &-x & = &23\\\Leftrightarrow & \color{red}{-}x & = &23\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{23}{-1} \\\Leftrightarrow & \color{green}{ x = -23 } & & \\ & V = \left\{ -23 \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{+12}& = & -10 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{+12}\color{blue}{-12-3x } & = & -10 \color{red}{ +3x }\color{blue}{-12-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & -10 \color{blue}{-12} \\\Leftrightarrow &-8x & = &-22\\\Leftrightarrow & \color{red}{-8}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-22}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{11}{4} } & & \\ & V = \left\{ \frac{11}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{+3}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+3}\color{blue}{-3-x } & = & -10 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & -10 \color{blue}{-3} \\\Leftrightarrow &9x & = &-13\\\Leftrightarrow & \color{red}{9}x & = &-13\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-13}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{9} } & & \\ & V = \left\{ \frac{-13}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{+7}& = & 3 \color{red}{ +7x } \\\Leftrightarrow & 9x \color{red}{+7}\color{blue}{-7-7x } & = & 3 \color{red}{ +7x }\color{blue}{-7-7x } \\\Leftrightarrow & 9x \color{blue}{-7x } & = & 3 \color{blue}{-7} \\\Leftrightarrow &2x & = &-4\\\Leftrightarrow & \color{red}{2}x & = &-4\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-4}{2} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{-5}& = & -14 \color{red}{ -15x } \\\Leftrightarrow & -x \color{red}{-5}\color{blue}{+5+15x } & = & -14 \color{red}{ -15x }\color{blue}{+5+15x } \\\Leftrightarrow & -x \color{blue}{+15x } & = & -14 \color{blue}{+5} \\\Leftrightarrow &14x & = &-9\\\Leftrightarrow & \color{red}{14}x & = &-9\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-9}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{14} } & & \\ & V = \left\{ \frac{-9}{14} \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{-7}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-7}\color{blue}{+7-x } & = & 11 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 11 \color{blue}{+7} \\\Leftrightarrow &-11x & = &18\\\Leftrightarrow & \color{red}{-11}x & = &18\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{18}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{11} } & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)