Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{-13}& = & -6 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{-13}\color{blue}{+13+2x } & = & -6 \color{red}{ -2x }\color{blue}{+13+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & -6 \color{blue}{+13} \\\Leftrightarrow &5x & = &7\\\Leftrightarrow & \color{red}{5}x & = &7\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{7}{5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{-1}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-1}\color{blue}{+1-x } & = & 3 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 3 \color{blue}{+1} \\\Leftrightarrow &-11x & = &4\\\Leftrightarrow & \color{red}{-11}x & = &4\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{4}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{+11}& = & 11 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{+11}\color{blue}{-11-x } & = & 11 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & 11 \color{blue}{-11} \\\Leftrightarrow &3x & = &0\\\Leftrightarrow & \color{red}{3}x & = &0\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{0}{3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{+13}& = & 3 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{+13}\color{blue}{-13-7x } & = & 3 \color{red}{ +7x }\color{blue}{-13-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & 3 \color{blue}{-13} \\\Leftrightarrow &-5x & = &-10\\\Leftrightarrow & \color{red}{-5}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-10}{-5} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{+1}& = & 5 \color{red}{ -5x } \\\Leftrightarrow & 8x \color{red}{+1}\color{blue}{-1+5x } & = & 5 \color{red}{ -5x }\color{blue}{-1+5x } \\\Leftrightarrow & 8x \color{blue}{+5x } & = & 5 \color{blue}{-1} \\\Leftrightarrow &13x & = &4\\\Leftrightarrow & \color{red}{13}x & = &4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{-6}& = & 14 \color{red}{ -3x } \\\Leftrightarrow & 13x \color{red}{-6}\color{blue}{+6+3x } & = & 14 \color{red}{ -3x }\color{blue}{+6+3x } \\\Leftrightarrow & 13x \color{blue}{+3x } & = & 14 \color{blue}{+6} \\\Leftrightarrow &16x & = &20\\\Leftrightarrow & \color{red}{16}x & = &20\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{20}{16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{-5}& = & -15 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-5}\color{blue}{+5-7x } & = & -15 \color{red}{ +7x }\color{blue}{+5-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -15 \color{blue}{+5} \\\Leftrightarrow &-13x & = &-10\\\Leftrightarrow & \color{red}{-13}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{+11}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+11}\color{blue}{-11-x } & = & 10 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 10 \color{blue}{-11} \\\Leftrightarrow &-5x & = &-1\\\Leftrightarrow & \color{red}{-5}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{+9}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+9}\color{blue}{-9-x } & = & 9 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 9 \color{blue}{-9} \\\Leftrightarrow &-11x & = &0\\\Leftrightarrow & \color{red}{-11}x & = &0\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{0}{-11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{-12}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-12}\color{blue}{+12-x } & = & 14 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 14 \color{blue}{+12} \\\Leftrightarrow &-6x & = &26\\\Leftrightarrow & \color{red}{-6}x & = &26\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{26}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{3} } & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{-13}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-13}\color{blue}{+13-x } & = & 7 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 7 \color{blue}{+13} \\\Leftrightarrow &-16x & = &20\\\Leftrightarrow & \color{red}{-16}x & = &20\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{20}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{+12}& = & -11 \color{red}{ +3x } \\\Leftrightarrow & 5x \color{red}{+12}\color{blue}{-12-3x } & = & -11 \color{red}{ +3x }\color{blue}{-12-3x } \\\Leftrightarrow & 5x \color{blue}{-3x } & = & -11 \color{blue}{-12} \\\Leftrightarrow &2x & = &-23\\\Leftrightarrow & \color{red}{2}x & = &-23\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-23}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{2} } & & \\ & V = \left\{ \frac{-23}{2} \right\} & \\\end{align}\)