Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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