Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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