Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{-6}& = & -10 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{-6}\color{blue}{+6+13x } & = & -10 \color{red}{ -13x }\color{blue}{+6+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & -10 \color{blue}{+6} \\\Leftrightarrow &22x & = &-4\\\Leftrightarrow & \color{red}{22}x & = &-4\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-4}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{-13}& = & 5 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-13}\color{blue}{+13-13x } & = & 5 \color{red}{ +13x }\color{blue}{+13-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 5 \color{blue}{+13} \\\Leftrightarrow &-19x & = &18\\\Leftrightarrow & \color{red}{-19}x & = &18\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{18}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{19} } & & \\ & V = \left\{ \frac{-18}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{-6}& = & -1 \color{red}{ -4x } \\\Leftrightarrow & -x \color{red}{-6}\color{blue}{+6+4x } & = & -1 \color{red}{ -4x }\color{blue}{+6+4x } \\\Leftrightarrow & -x \color{blue}{+4x } & = & -1 \color{blue}{+6} \\\Leftrightarrow &3x & = &5\\\Leftrightarrow & \color{red}{3}x & = &5\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{5}{3} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{-11}& = & 7 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-11}\color{blue}{+11-7x } & = & 7 \color{red}{ +7x }\color{blue}{+11-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & 7 \color{blue}{+11} \\\Leftrightarrow &-13x & = &18\\\Leftrightarrow & \color{red}{-13}x & = &18\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{18}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{13} } & & \\ & V = \left\{ \frac{-18}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{+11}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+11}\color{blue}{-11-x } & = & -14 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -14 \color{blue}{-11} \\\Leftrightarrow &-16x & = &-25\\\Leftrightarrow & \color{red}{-16}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-25}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{25}{16} } & & \\ & V = \left\{ \frac{25}{16} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{+13}& = & -3 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{+13}\color{blue}{-13+8x } & = & -3 \color{red}{ -8x }\color{blue}{-13+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & -3 \color{blue}{-13} \\\Leftrightarrow &11x & = &-16\\\Leftrightarrow & \color{red}{11}x & = &-16\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-16}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{11} } & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{-12}& = & -2 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12+8x } & = & -2 \color{red}{ -8x }\color{blue}{+12+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & -2 \color{blue}{+12} \\\Leftrightarrow &11x & = &10\\\Leftrightarrow & \color{red}{11}x & = &10\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{10}{11} \\\Leftrightarrow & \color{green}{ x = \frac{10}{11} } & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+9}& = & 10 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{+9}\color{blue}{-9-11x } & = & 10 \color{red}{ +11x }\color{blue}{-9-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & 10 \color{blue}{-9} \\\Leftrightarrow &-21x & = &1\\\Leftrightarrow & \color{red}{-21}x & = &1\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{1}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{21} } & & \\ & V = \left\{ \frac{-1}{21} \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{-12}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-12}\color{blue}{+12-x } & = & 13 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 13 \color{blue}{+12} \\\Leftrightarrow &-6x & = &25\\\Leftrightarrow & \color{red}{-6}x & = &25\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{25}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{6} } & & \\ & V = \left\{ \frac{-25}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{-10}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-10}\color{blue}{+10-x } & = & -13 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -13 \color{blue}{+10} \\\Leftrightarrow &-12x & = &-3\\\Leftrightarrow & \color{red}{-12}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-3}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & 2x \color{red}{-3}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-3}\color{blue}{+3-x } & = & -15 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -15 \color{blue}{+3} \\\Leftrightarrow &x & = &-12\\\Leftrightarrow & \color{red}{}x & = &-12\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -12 \\\Leftrightarrow & \color{green}{ x = -12 } & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{+1}& = & 2 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+1}\color{blue}{-1-7x } & = & 2 \color{red}{ +7x }\color{blue}{-1-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 2 \color{blue}{-1} \\\Leftrightarrow &3x & = &1\\\Leftrightarrow & \color{red}{3}x & = &1\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{1}{3} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)