Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{+5}& = & -13 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+5}\color{blue}{-5-7x } & = & -13 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -13 \color{blue}{-5} \\\Leftrightarrow &-13x & = &-18\\\Leftrightarrow & \color{red}{-13}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-18}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{18}{13} } & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{-10}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-10}\color{blue}{+10-13x } & = & 9 \color{red}{ +13x }\color{blue}{+10-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 9 \color{blue}{+10} \\\Leftrightarrow &-25x & = &19\\\Leftrightarrow & \color{red}{-25}x & = &19\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{19}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{25} } & & \\ & V = \left\{ \frac{-19}{25} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{-14}& = & 15 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{-14}\color{blue}{+14-7x } & = & 15 \color{red}{ +7x }\color{blue}{+14-7x } \\\Leftrightarrow & 12x \color{blue}{-7x } & = & 15 \color{blue}{+14} \\\Leftrightarrow &5x & = &29\\\Leftrightarrow & \color{red}{5}x & = &29\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{29}{5} \\\Leftrightarrow & \color{green}{ x = \frac{29}{5} } & & \\ & V = \left\{ \frac{29}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{+10}& = & 13 \color{red}{ +4x } \\\Leftrightarrow & -11x \color{red}{+10}\color{blue}{-10-4x } & = & 13 \color{red}{ +4x }\color{blue}{-10-4x } \\\Leftrightarrow & -11x \color{blue}{-4x } & = & 13 \color{blue}{-10} \\\Leftrightarrow &-15x & = &3\\\Leftrightarrow & \color{red}{-15}x & = &3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{+13}& = & -14 \color{red}{ +10x } \\\Leftrightarrow & 11x \color{red}{+13}\color{blue}{-13-10x } & = & -14 \color{red}{ +10x }\color{blue}{-13-10x } \\\Leftrightarrow & 11x \color{blue}{-10x } & = & -14 \color{blue}{-13} \\\Leftrightarrow &x & = &-27\\\Leftrightarrow & \color{red}{}x & = &-27\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -27 \\\Leftrightarrow & \color{green}{ x = -27 } & & \\ & V = \left\{ -27 \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{+7}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+7}\color{blue}{-7-x } & = & -14 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -14 \color{blue}{-7} \\\Leftrightarrow &-11x & = &-21\\\Leftrightarrow & \color{red}{-11}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-21}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{21}{11} } & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{+14}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+14}\color{blue}{-14-x } & = & 14 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 14 \color{blue}{-14} \\\Leftrightarrow &-9x & = &0\\\Leftrightarrow & \color{red}{-9}x & = &0\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{0}{-9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{-10}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-10}\color{blue}{+10-x } & = & 13 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 13 \color{blue}{+10} \\\Leftrightarrow &-9x & = &23\\\Leftrightarrow & \color{red}{-9}x & = &23\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{23}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{9} } & & \\ & V = \left\{ \frac{-23}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{+11}& = & -4 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{+11}\color{blue}{-11-10x } & = & -4 \color{red}{ +10x }\color{blue}{-11-10x } \\\Leftrightarrow & 9x \color{blue}{-10x } & = & -4 \color{blue}{-11} \\\Leftrightarrow &-x & = &-15\\\Leftrightarrow & \color{red}{-}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-15}{-1} \\\Leftrightarrow & \color{green}{ x = 15 } & & \\ & V = \left\{ 15 \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{+10}& = & 2 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+10}\color{blue}{-10+5x } & = & 2 \color{red}{ -5x }\color{blue}{-10+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 2 \color{blue}{-10} \\\Leftrightarrow &11x & = &-8\\\Leftrightarrow & \color{red}{11}x & = &-8\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-8}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{11} } & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{+3}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+3}\color{blue}{-3-x } & = & 8 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 8 \color{blue}{-3} \\\Leftrightarrow &-8x & = &5\\\Leftrightarrow & \color{red}{-8}x & = &5\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{5}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{-12}& = & 3 \color{red}{ +8x } \\\Leftrightarrow & -x \color{red}{-12}\color{blue}{+12-8x } & = & 3 \color{red}{ +8x }\color{blue}{+12-8x } \\\Leftrightarrow & -x \color{blue}{-8x } & = & 3 \color{blue}{+12} \\\Leftrightarrow &-9x & = &15\\\Leftrightarrow & \color{red}{-9}x & = &15\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{15}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)