Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{-4}& = & 12 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-4}\color{blue}{+4-7x } & = & 12 \color{red}{ +7x }\color{blue}{+4-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & 12 \color{blue}{+4} \\\Leftrightarrow &-13x & = &16\\\Leftrightarrow & \color{red}{-13}x & = &16\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{16}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{13} } & & \\ & V = \left\{ \frac{-16}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{+12}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+12}\color{blue}{-12-x } & = & 8 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & 8 \color{blue}{-12} \\\Leftrightarrow &9x & = &-4\\\Leftrightarrow & \color{red}{9}x & = &-4\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-4}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{9} } & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{-5}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-5}\color{blue}{+5-x } & = & -5 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -5 \color{blue}{+5} \\\Leftrightarrow &-14x & = &0\\\Leftrightarrow & \color{red}{-14}x & = &0\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{0}{-14} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{+12}& = & 4 \color{red}{ +2x } \\\Leftrightarrow & 13x \color{red}{+12}\color{blue}{-12-2x } & = & 4 \color{red}{ +2x }\color{blue}{-12-2x } \\\Leftrightarrow & 13x \color{blue}{-2x } & = & 4 \color{blue}{-12} \\\Leftrightarrow &11x & = &-8\\\Leftrightarrow & \color{red}{11}x & = &-8\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-8}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{11} } & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{-3}& = & -2 \color{red}{ -11x } \\\Leftrightarrow & x \color{red}{-3}\color{blue}{+3+11x } & = & -2 \color{red}{ -11x }\color{blue}{+3+11x } \\\Leftrightarrow & x \color{blue}{+11x } & = & -2 \color{blue}{+3} \\\Leftrightarrow &12x & = &1\\\Leftrightarrow & \color{red}{12}x & = &1\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{1}{12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{12} } & & \\ & V = \left\{ \frac{1}{12} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{+12}& = & -5 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{+12}\color{blue}{-12-11x } & = & -5 \color{red}{ +11x }\color{blue}{-12-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & -5 \color{blue}{-12} \\\Leftrightarrow &-9x & = &-17\\\Leftrightarrow & \color{red}{-9}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-17}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{17}{9} } & & \\ & V = \left\{ \frac{17}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{+3}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+3}\color{blue}{-3-x } & = & -8 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -8 \color{blue}{-3} \\\Leftrightarrow &-11x & = &-11\\\Leftrightarrow & \color{red}{-11}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-11}{-11} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{-12}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-12}\color{blue}{+12-x } & = & -6 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -6 \color{blue}{+12} \\\Leftrightarrow &-13x & = &6\\\Leftrightarrow & \color{red}{-13}x & = &6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{+2}& = & -8 \color{red}{ +2x } \\\Leftrightarrow & 5x \color{red}{+2}\color{blue}{-2-2x } & = & -8 \color{red}{ +2x }\color{blue}{-2-2x } \\\Leftrightarrow & 5x \color{blue}{-2x } & = & -8 \color{blue}{-2} \\\Leftrightarrow &3x & = &-10\\\Leftrightarrow & \color{red}{3}x & = &-10\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-10}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{3} } & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{+3}& = & -3 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+3}\color{blue}{-3-5x } & = & -3 \color{red}{ +5x }\color{blue}{-3-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & -3 \color{blue}{-3} \\\Leftrightarrow &-9x & = &-6\\\Leftrightarrow & \color{red}{-9}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{+4}& = & -14 \color{red}{ +7x } \\\Leftrightarrow & 6x \color{red}{+4}\color{blue}{-4-7x } & = & -14 \color{red}{ +7x }\color{blue}{-4-7x } \\\Leftrightarrow & 6x \color{blue}{-7x } & = & -14 \color{blue}{-4} \\\Leftrightarrow &-x & = &-18\\\Leftrightarrow & \color{red}{-}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-18}{-1} \\\Leftrightarrow & \color{green}{ x = 18 } & & \\ & V = \left\{ 18 \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{-5}& = & -3 \color{red}{ +2x } \\\Leftrightarrow & -x \color{red}{-5}\color{blue}{+5-2x } & = & -3 \color{red}{ +2x }\color{blue}{+5-2x } \\\Leftrightarrow & -x \color{blue}{-2x } & = & -3 \color{blue}{+5} \\\Leftrightarrow &-3x & = &2\\\Leftrightarrow & \color{red}{-3}x & = &2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)