Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{+4}& = & -2 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{+4}\color{blue}{-4+12x } & = & -2 \color{red}{ -12x }\color{blue}{-4+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & -2 \color{blue}{-4} \\\Leftrightarrow &25x & = &-6\\\Leftrightarrow & \color{red}{25}x & = &-6\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-6}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{25} } & & \\ & V = \left\{ \frac{-6}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & 13x \color{red}{-2}& = & 8 \color{red}{ -2x } \\\Leftrightarrow & 13x \color{red}{-2}\color{blue}{+2+2x } & = & 8 \color{red}{ -2x }\color{blue}{+2+2x } \\\Leftrightarrow & 13x \color{blue}{+2x } & = & 8 \color{blue}{+2} \\\Leftrightarrow &15x & = &10\\\Leftrightarrow & \color{red}{15}x & = &10\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{10}{15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{+3}& = & -1 \color{red}{ -13x } \\\Leftrightarrow & 8x \color{red}{+3}\color{blue}{-3+13x } & = & -1 \color{red}{ -13x }\color{blue}{-3+13x } \\\Leftrightarrow & 8x \color{blue}{+13x } & = & -1 \color{blue}{-3} \\\Leftrightarrow &21x & = &-4\\\Leftrightarrow & \color{red}{21}x & = &-4\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-4}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{21} } & & \\ & V = \left\{ \frac{-4}{21} \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{-13}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-13}\color{blue}{+13-x } & = & 13 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 13 \color{blue}{+13} \\\Leftrightarrow &13x & = &26\\\Leftrightarrow & \color{red}{13}x & = &26\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{26}{13} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+5}& = & -7 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+5}\color{blue}{-5-9x } & = & -7 \color{red}{ +9x }\color{blue}{-5-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -7 \color{blue}{-5} \\\Leftrightarrow &-17x & = &-12\\\Leftrightarrow & \color{red}{-17}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-12}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{12}{17} } & & \\ & V = \left\{ \frac{12}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{-4}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-4}\color{blue}{+4-x } & = & -12 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -12 \color{blue}{+4} \\\Leftrightarrow &x & = &-8\\\Leftrightarrow & \color{red}{}x & = &-8\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -8 \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{-13}& = & -13 \color{red}{ -2x } \\\Leftrightarrow & 9x \color{red}{-13}\color{blue}{+13+2x } & = & -13 \color{red}{ -2x }\color{blue}{+13+2x } \\\Leftrightarrow & 9x \color{blue}{+2x } & = & -13 \color{blue}{+13} \\\Leftrightarrow &11x & = &0\\\Leftrightarrow & \color{red}{11}x & = &0\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{0}{11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{-9}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-9}\color{blue}{+9-x } & = & -8 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -8 \color{blue}{+9} \\\Leftrightarrow &-3x & = &1\\\Leftrightarrow & \color{red}{-3}x & = &1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{+8}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+8}\color{blue}{-8-x } & = & -1 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -1 \color{blue}{-8} \\\Leftrightarrow &-11x & = &-9\\\Leftrightarrow & \color{red}{-11}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{-13}& = & -11 \color{red}{ +5x } \\\Leftrightarrow & 8x \color{red}{-13}\color{blue}{+13-5x } & = & -11 \color{red}{ +5x }\color{blue}{+13-5x } \\\Leftrightarrow & 8x \color{blue}{-5x } & = & -11 \color{blue}{+13} \\\Leftrightarrow &3x & = &2\\\Leftrightarrow & \color{red}{3}x & = &2\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{2}{3} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{-8}& = & -13 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{-8}\color{blue}{+8+3x } & = & -13 \color{red}{ -3x }\color{blue}{+8+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & -13 \color{blue}{+8} \\\Leftrightarrow &10x & = &-5\\\Leftrightarrow & \color{red}{10}x & = &-5\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-5}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{+7}& = & 5 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+7}\color{blue}{-7-5x } & = & 5 \color{red}{ +5x }\color{blue}{-7-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & 5 \color{blue}{-7} \\\Leftrightarrow &7x & = &-2\\\Leftrightarrow & \color{red}{7}x & = &-2\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-2}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)