Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{-6}& = & 3 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-6}\color{blue}{+6+11x } & = & 3 \color{red}{ -11x }\color{blue}{+6+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 3 \color{blue}{+6} \\\Leftrightarrow &23x & = &9\\\Leftrightarrow & \color{red}{23}x & = &9\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{9}{23} \\\Leftrightarrow & \color{green}{ x = \frac{9}{23} } & & \\ & V = \left\{ \frac{9}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{+12}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+12}\color{blue}{-12-x } & = & -8 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -8 \color{blue}{-12} \\\Leftrightarrow &-5x & = &-20\\\Leftrightarrow & \color{red}{-5}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-20}{-5} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{-7}& = & -5 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{-7}\color{blue}{+7-x } & = & -5 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & -5 \color{blue}{+7} \\\Leftrightarrow &2x & = &2\\\Leftrightarrow & \color{red}{2}x & = &2\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{2}{2} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{+13}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+13}\color{blue}{-13-x } & = & -9 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -9 \color{blue}{-13} \\\Leftrightarrow &-3x & = &-22\\\Leftrightarrow & \color{red}{-3}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-22}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{22}{3} } & & \\ & V = \left\{ \frac{22}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -10x \color{red}{+3}& = & 12 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{+3}\color{blue}{-3-11x } & = & 12 \color{red}{ +11x }\color{blue}{-3-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & 12 \color{blue}{-3} \\\Leftrightarrow &-21x & = &9\\\Leftrightarrow & \color{red}{-21}x & = &9\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{9}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{+13}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+13}\color{blue}{-13-x } & = & 1 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 1 \color{blue}{-13} \\\Leftrightarrow &-16x & = &-12\\\Leftrightarrow & \color{red}{-16}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-12}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{-2}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-2}\color{blue}{+2-x } & = & -6 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -6 \color{blue}{+2} \\\Leftrightarrow &-6x & = &-4\\\Leftrightarrow & \color{red}{-6}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-4}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{-11}& = & 11 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{-11}\color{blue}{+11-11x } & = & 11 \color{red}{ +11x }\color{blue}{+11-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & 11 \color{blue}{+11} \\\Leftrightarrow &-21x & = &22\\\Leftrightarrow & \color{red}{-21}x & = &22\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{22}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{21} } & & \\ & V = \left\{ \frac{-22}{21} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{+10}& = & -2 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{+10}\color{blue}{-10+4x } & = & -2 \color{red}{ -4x }\color{blue}{-10+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -2 \color{blue}{-10} \\\Leftrightarrow &13x & = &-12\\\Leftrightarrow & \color{red}{13}x & = &-12\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-12}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{+3}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+3}\color{blue}{-3-x } & = & -4 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -4 \color{blue}{-3} \\\Leftrightarrow &-5x & = &-7\\\Leftrightarrow & \color{red}{-5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{-6}& = & 13 \color{red}{ +8x } \\\Leftrightarrow & 7x \color{red}{-6}\color{blue}{+6-8x } & = & 13 \color{red}{ +8x }\color{blue}{+6-8x } \\\Leftrightarrow & 7x \color{blue}{-8x } & = & 13 \color{blue}{+6} \\\Leftrightarrow &-x & = &19\\\Leftrightarrow & \color{red}{-}x & = &19\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{19}{-1} \\\Leftrightarrow & \color{green}{ x = -19 } & & \\ & V = \left\{ -19 \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{-6}& = & -5 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-6}\color{blue}{+6+13x } & = & -5 \color{red}{ -13x }\color{blue}{+6+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -5 \color{blue}{+6} \\\Leftrightarrow &23x & = &1\\\Leftrightarrow & \color{red}{23}x & = &1\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{1}{23} \\\Leftrightarrow & \color{green}{ x = \frac{1}{23} } & & \\ & V = \left\{ \frac{1}{23} \right\} & \\\end{align}\)