Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{-8}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{-8}\color{blue}{+8-13x } & = & 13 \color{red}{ +13x }\color{blue}{+8-13x } \\\Leftrightarrow & 12x \color{blue}{-13x } & = & 13 \color{blue}{+8} \\\Leftrightarrow &-x & = &21\\\Leftrightarrow & \color{red}{-}x & = &21\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{21}{-1} \\\Leftrightarrow & \color{green}{ x = -21 } & & \\ & V = \left\{ -21 \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{+2}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+2}\color{blue}{-2-x } & = & -4 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -4 \color{blue}{-2} \\\Leftrightarrow &x & = &-6\\\Leftrightarrow & \color{red}{}x & = &-6\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -6 \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{+10}& = & -5 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{+10}\color{blue}{-10-9x } & = & -5 \color{red}{ +9x }\color{blue}{-10-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & -5 \color{blue}{-10} \\\Leftrightarrow &-13x & = &-15\\\Leftrightarrow & \color{red}{-13}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-15}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{15}{13} } & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{+4}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+4}\color{blue}{-4-x } & = & -14 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -14 \color{blue}{-4} \\\Leftrightarrow &-11x & = &-18\\\Leftrightarrow & \color{red}{-11}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-18}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{18}{11} } & & \\ & V = \left\{ \frac{18}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{+6}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+6}\color{blue}{-6-x } & = & -8 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -8 \color{blue}{-6} \\\Leftrightarrow &-4x & = &-14\\\Leftrightarrow & \color{red}{-4}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-14}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{-15}& = & 5 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{-15}\color{blue}{+15-3x } & = & 5 \color{red}{ +3x }\color{blue}{+15-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & 5 \color{blue}{+15} \\\Leftrightarrow &-x & = &20\\\Leftrightarrow & \color{red}{-}x & = &20\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{20}{-1} \\\Leftrightarrow & \color{green}{ x = -20 } & & \\ & V = \left\{ -20 \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{-14}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-14}\color{blue}{+14-x } & = & -13 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -13 \color{blue}{+14} \\\Leftrightarrow &-4x & = &1\\\Leftrightarrow & \color{red}{-4}x & = &1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{+15}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{+15}\color{blue}{-15-x } & = & 6 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & 6 \color{blue}{-15} \\\Leftrightarrow &12x & = &-9\\\Leftrightarrow & \color{red}{12}x & = &-9\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-9}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{+13}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+13}\color{blue}{-13-x } & = & 2 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 2 \color{blue}{-13} \\\Leftrightarrow &-8x & = &-11\\\Leftrightarrow & \color{red}{-8}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-11}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{11}{8} } & & \\ & V = \left\{ \frac{11}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{-8}& = & -13 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-8}\color{blue}{+8-7x } & = & -13 \color{red}{ +7x }\color{blue}{+8-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & -13 \color{blue}{+8} \\\Leftrightarrow &3x & = &-5\\\Leftrightarrow & \color{red}{3}x & = &-5\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-5}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{+2}& = & 14 \color{red}{ -15x } \\\Leftrightarrow & x \color{red}{+2}\color{blue}{-2+15x } & = & 14 \color{red}{ -15x }\color{blue}{-2+15x } \\\Leftrightarrow & x \color{blue}{+15x } & = & 14 \color{blue}{-2} \\\Leftrightarrow &16x & = &12\\\Leftrightarrow & \color{red}{16}x & = &12\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{12}{16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{+9}& = & 9 \color{red}{ -9x } \\\Leftrightarrow & x \color{red}{+9}\color{blue}{-9+9x } & = & 9 \color{red}{ -9x }\color{blue}{-9+9x } \\\Leftrightarrow & x \color{blue}{+9x } & = & 9 \color{blue}{-9} \\\Leftrightarrow &10x & = &0\\\Leftrightarrow & \color{red}{10}x & = &0\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{0}{10} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)