Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{-6}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-6}\color{blue}{+6-x } & = & -5 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -5 \color{blue}{+6} \\\Leftrightarrow &-8x & = &1\\\Leftrightarrow & \color{red}{-8}x & = &1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{+13}& = & -4 \color{red}{ +13x } \\\Leftrightarrow & 14x \color{red}{+13}\color{blue}{-13-13x } & = & -4 \color{red}{ +13x }\color{blue}{-13-13x } \\\Leftrightarrow & 14x \color{blue}{-13x } & = & -4 \color{blue}{-13} \\\Leftrightarrow &x & = &-17\\\Leftrightarrow & \color{red}{}x & = &-17\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -17 \\\Leftrightarrow & \color{green}{ x = -17 } & & \\ & V = \left\{ -17 \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{+11}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+11}\color{blue}{-11-x } & = & -10 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -10 \color{blue}{-11} \\\Leftrightarrow &-11x & = &-21\\\Leftrightarrow & \color{red}{-11}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-21}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{21}{11} } & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{+13}& = & 3 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{+13}\color{blue}{-13+11x } & = & 3 \color{red}{ -11x }\color{blue}{-13+11x } \\\Leftrightarrow & 14x \color{blue}{+11x } & = & 3 \color{blue}{-13} \\\Leftrightarrow &25x & = &-10\\\Leftrightarrow & \color{red}{25}x & = &-10\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-10}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{+8}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+8}\color{blue}{-8-x } & = & -10 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -10 \color{blue}{-8} \\\Leftrightarrow &-13x & = &-18\\\Leftrightarrow & \color{red}{-13}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-18}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{18}{13} } & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{-1}& = & 10 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-1}\color{blue}{+1+2x } & = & 10 \color{red}{ -2x }\color{blue}{+1+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 10 \color{blue}{+1} \\\Leftrightarrow &17x & = &11\\\Leftrightarrow & \color{red}{17}x & = &11\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{11}{17} \\\Leftrightarrow & \color{green}{ x = \frac{11}{17} } & & \\ & V = \left\{ \frac{11}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{+13}& = & 9 \color{red}{ -15x } \\\Leftrightarrow & -x \color{red}{+13}\color{blue}{-13+15x } & = & 9 \color{red}{ -15x }\color{blue}{-13+15x } \\\Leftrightarrow & -x \color{blue}{+15x } & = & 9 \color{blue}{-13} \\\Leftrightarrow &14x & = &-4\\\Leftrightarrow & \color{red}{14}x & = &-4\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-4}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{-3}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-3}\color{blue}{+3-x } & = & -13 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -13 \color{blue}{+3} \\\Leftrightarrow &x & = &-10\\\Leftrightarrow & \color{red}{}x & = &-10\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -10 \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{-4}& = & -1 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{-4}\color{blue}{+4+6x } & = & -1 \color{red}{ -6x }\color{blue}{+4+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & -1 \color{blue}{+4} \\\Leftrightarrow &13x & = &3\\\Leftrightarrow & \color{red}{13}x & = &3\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{3}{13} \\\Leftrightarrow & \color{green}{ x = \frac{3}{13} } & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{+10}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+10}\color{blue}{-10-x } & = & 2 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 2 \color{blue}{-10} \\\Leftrightarrow &-15x & = &-8\\\Leftrightarrow & \color{red}{-15}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{8}{15} } & & \\ & V = \left\{ \frac{8}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{-5}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-5}\color{blue}{+5-x } & = & 11 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 11 \color{blue}{+5} \\\Leftrightarrow &-8x & = &16\\\Leftrightarrow & \color{red}{-8}x & = &16\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{16}{-8} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{+6}& = & -12 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{+6}\color{blue}{-6-3x } & = & -12 \color{red}{ +3x }\color{blue}{-6-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & -12 \color{blue}{-6} \\\Leftrightarrow &-x & = &-18\\\Leftrightarrow & \color{red}{-}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-18}{-1} \\\Leftrightarrow & \color{green}{ x = 18 } & & \\ & V = \left\{ 18 \right\} & \\\end{align}\)