Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{+3}& = & 5 \color{red}{ +13x } \\\Leftrightarrow & x \color{red}{+3}\color{blue}{-3-13x } & = & 5 \color{red}{ +13x }\color{blue}{-3-13x } \\\Leftrightarrow & x \color{blue}{-13x } & = & 5 \color{blue}{-3} \\\Leftrightarrow &-12x & = &2\\\Leftrightarrow & \color{red}{-12}x & = &2\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{2}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{-4}& = & -2 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{-4}\color{blue}{+4+3x } & = & -2 \color{red}{ -3x }\color{blue}{+4+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & -2 \color{blue}{+4} \\\Leftrightarrow &10x & = &2\\\Leftrightarrow & \color{red}{10}x & = &2\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{2}{10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{+3}& = & 13 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+3}\color{blue}{-3-5x } & = & 13 \color{red}{ +5x }\color{blue}{-3-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & 13 \color{blue}{-3} \\\Leftrightarrow &-14x & = &10\\\Leftrightarrow & \color{red}{-14}x & = &10\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{10}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{-4}& = & -9 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{-4}\color{blue}{+4-4x } & = & -9 \color{red}{ +4x }\color{blue}{+4-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & -9 \color{blue}{+4} \\\Leftrightarrow &-7x & = &-5\\\Leftrightarrow & \color{red}{-7}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-5}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{-13}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & 4x \color{red}{-13}\color{blue}{+13-7x } & = & 11 \color{red}{ +7x }\color{blue}{+13-7x } \\\Leftrightarrow & 4x \color{blue}{-7x } & = & 11 \color{blue}{+13} \\\Leftrightarrow &-3x & = &24\\\Leftrightarrow & \color{red}{-3}x & = &24\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{24}{-3} \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{+8}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+8}\color{blue}{-8-x } & = & -3 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -3 \color{blue}{-8} \\\Leftrightarrow &-16x & = &-11\\\Leftrightarrow & \color{red}{-16}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-11}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{11}{16} } & & \\ & V = \left\{ \frac{11}{16} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{-3}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-3}\color{blue}{+3-x } & = & 3 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 3 \color{blue}{+3} \\\Leftrightarrow &-5x & = &6\\\Leftrightarrow & \color{red}{-5}x & = &6\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{6}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{+13}& = & -8 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+13}\color{blue}{-13-13x } & = & -8 \color{red}{ +13x }\color{blue}{-13-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -8 \color{blue}{-13} \\\Leftrightarrow &-25x & = &-21\\\Leftrightarrow & \color{red}{-25}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-21}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{21}{25} } & & \\ & V = \left\{ \frac{21}{25} \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{-4}& = & -5 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-4}\color{blue}{+4+8x } & = & -5 \color{red}{ -8x }\color{blue}{+4+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & -5 \color{blue}{+4} \\\Leftrightarrow &11x & = &-1\\\Leftrightarrow & \color{red}{11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{+9}& = & 3 \color{red}{ +5x } \\\Leftrightarrow & 2x \color{red}{+9}\color{blue}{-9-5x } & = & 3 \color{red}{ +5x }\color{blue}{-9-5x } \\\Leftrightarrow & 2x \color{blue}{-5x } & = & 3 \color{blue}{-9} \\\Leftrightarrow &-3x & = &-6\\\Leftrightarrow & \color{red}{-3}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-6}{-3} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{+3}& = & -4 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+3}\color{blue}{-3+7x } & = & -4 \color{red}{ -7x }\color{blue}{-3+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -4 \color{blue}{-3} \\\Leftrightarrow &15x & = &-7\\\Leftrightarrow & \color{red}{15}x & = &-7\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-7}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{15} } & & \\ & V = \left\{ \frac{-7}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{+4}& = & 6 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{+4}\color{blue}{-4-7x } & = & 6 \color{red}{ +7x }\color{blue}{-4-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & 6 \color{blue}{-4} \\\Leftrightarrow &-5x & = &2\\\Leftrightarrow & \color{red}{-5}x & = &2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)