Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{-8}& = & 15 \color{red}{ +13x } \\\Leftrightarrow & 15x \color{red}{-8}\color{blue}{+8-13x } & = & 15 \color{red}{ +13x }\color{blue}{+8-13x } \\\Leftrightarrow & 15x \color{blue}{-13x } & = & 15 \color{blue}{+8} \\\Leftrightarrow &2x & = &23\\\Leftrightarrow & \color{red}{2}x & = &23\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{23}{2} \\\Leftrightarrow & \color{green}{ x = \frac{23}{2} } & & \\ & V = \left\{ \frac{23}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{-12}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-12}\color{blue}{+12-x } & = & -4 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -4 \color{blue}{+12} \\\Leftrightarrow &-12x & = &8\\\Leftrightarrow & \color{red}{-12}x & = &8\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{8}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{-5}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-5}\color{blue}{+5-x } & = & -6 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -6 \color{blue}{+5} \\\Leftrightarrow &-13x & = &-1\\\Leftrightarrow & \color{red}{-13}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{+13}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & 4x \color{red}{+13}\color{blue}{-13-13x } & = & -7 \color{red}{ +13x }\color{blue}{-13-13x } \\\Leftrightarrow & 4x \color{blue}{-13x } & = & -7 \color{blue}{-13} \\\Leftrightarrow &-9x & = &-20\\\Leftrightarrow & \color{red}{-9}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-20}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{20}{9} } & & \\ & V = \left\{ \frac{20}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{-15}& = & 10 \color{red}{ -2x } \\\Leftrightarrow & 9x \color{red}{-15}\color{blue}{+15+2x } & = & 10 \color{red}{ -2x }\color{blue}{+15+2x } \\\Leftrightarrow & 9x \color{blue}{+2x } & = & 10 \color{blue}{+15} \\\Leftrightarrow &11x & = &25\\\Leftrightarrow & \color{red}{11}x & = &25\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{25}{11} \\\Leftrightarrow & \color{green}{ x = \frac{25}{11} } & & \\ & V = \left\{ \frac{25}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{+3}& = & 7 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{+3}\color{blue}{-3-5x } & = & 7 \color{red}{ +5x }\color{blue}{-3-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & 7 \color{blue}{-3} \\\Leftrightarrow &-17x & = &4\\\Leftrightarrow & \color{red}{-17}x & = &4\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{4}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{17} } & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{-12}& = & 8 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{-12}\color{blue}{+12-4x } & = & 8 \color{red}{ +4x }\color{blue}{+12-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & 8 \color{blue}{+12} \\\Leftrightarrow &-11x & = &20\\\Leftrightarrow & \color{red}{-11}x & = &20\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{20}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{11} } & & \\ & V = \left\{ \frac{-20}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{-12}& = & 8 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-12}\color{blue}{+12-13x } & = & 8 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 8 \color{blue}{+12} \\\Leftrightarrow &-25x & = &20\\\Leftrightarrow & \color{red}{-25}x & = &20\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{20}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{+6}& = & -14 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{+6}\color{blue}{-6+13x } & = & -14 \color{red}{ -13x }\color{blue}{-6+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & -14 \color{blue}{-6} \\\Leftrightarrow &22x & = &-20\\\Leftrightarrow & \color{red}{22}x & = &-20\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-20}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{11} } & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{+14}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+14}\color{blue}{-14-x } & = & -3 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -3 \color{blue}{-14} \\\Leftrightarrow &-13x & = &-17\\\Leftrightarrow & \color{red}{-13}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-17}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{17}{13} } & & \\ & V = \left\{ \frac{17}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{+3}& = & -12 \color{red}{ +4x } \\\Leftrightarrow & 11x \color{red}{+3}\color{blue}{-3-4x } & = & -12 \color{red}{ +4x }\color{blue}{-3-4x } \\\Leftrightarrow & 11x \color{blue}{-4x } & = & -12 \color{blue}{-3} \\\Leftrightarrow &7x & = &-15\\\Leftrightarrow & \color{red}{7}x & = &-15\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-15}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{7} } & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{-15}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & 6x \color{red}{-15}\color{blue}{+15-13x } & = & -7 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & 6x \color{blue}{-13x } & = & -7 \color{blue}{+15} \\\Leftrightarrow &-7x & = &8\\\Leftrightarrow & \color{red}{-7}x & = &8\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{8}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)