Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{-15}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-15}\color{blue}{+15-x } & = & -15 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -15 \color{blue}{+15} \\\Leftrightarrow &-13x & = &0\\\Leftrightarrow & \color{red}{-13}x & = &0\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{0}{-13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{+6}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+6}\color{blue}{-6-x } & = & -9 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -9 \color{blue}{-6} \\\Leftrightarrow &13x & = &-15\\\Leftrightarrow & \color{red}{13}x & = &-15\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-15}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{13} } & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{-13}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-13}\color{blue}{+13-x } & = & -14 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -14 \color{blue}{+13} \\\Leftrightarrow &x & = &-1\\\Leftrightarrow & \color{red}{}x & = &-1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -1 \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{-14}& = & 1 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{-14}\color{blue}{+14+11x } & = & 1 \color{red}{ -11x }\color{blue}{+14+11x } \\\Leftrightarrow & 14x \color{blue}{+11x } & = & 1 \color{blue}{+14} \\\Leftrightarrow &25x & = &15\\\Leftrightarrow & \color{red}{25}x & = &15\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{15}{25} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{+10}& = & -5 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+10}\color{blue}{-10+13x } & = & -5 \color{red}{ -13x }\color{blue}{-10+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -5 \color{blue}{-10} \\\Leftrightarrow &27x & = &-15\\\Leftrightarrow & \color{red}{27}x & = &-15\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-15}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{9} } & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{+8}& = & 2 \color{red}{ +13x } \\\Leftrightarrow & 3x \color{red}{+8}\color{blue}{-8-13x } & = & 2 \color{red}{ +13x }\color{blue}{-8-13x } \\\Leftrightarrow & 3x \color{blue}{-13x } & = & 2 \color{blue}{-8} \\\Leftrightarrow &-10x & = &-6\\\Leftrightarrow & \color{red}{-10}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-6}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{+10}& = & -5 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+10}\color{blue}{-10+13x } & = & -5 \color{red}{ -13x }\color{blue}{-10+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & -5 \color{blue}{-10} \\\Leftrightarrow &24x & = &-15\\\Leftrightarrow & \color{red}{24}x & = &-15\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-15}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{-7}& = & 7 \color{red}{ +13x } \\\Leftrightarrow & -5x \color{red}{-7}\color{blue}{+7-13x } & = & 7 \color{red}{ +13x }\color{blue}{+7-13x } \\\Leftrightarrow & -5x \color{blue}{-13x } & = & 7 \color{blue}{+7} \\\Leftrightarrow &-18x & = &14\\\Leftrightarrow & \color{red}{-18}x & = &14\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{14}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{9} } & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{+2}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+2}\color{blue}{-2-x } & = & 15 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 15 \color{blue}{-2} \\\Leftrightarrow &-6x & = &13\\\Leftrightarrow & \color{red}{-6}x & = &13\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{13}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{6} } & & \\ & V = \left\{ \frac{-13}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{+12}& = & 1 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{+12}\color{blue}{-12+3x } & = & 1 \color{red}{ -3x }\color{blue}{-12+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & 1 \color{blue}{-12} \\\Leftrightarrow &10x & = &-11\\\Leftrightarrow & \color{red}{10}x & = &-11\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-11}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{10} } & & \\ & V = \left\{ \frac{-11}{10} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{-4}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-4}\color{blue}{+4-x } & = & 11 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 11 \color{blue}{+4} \\\Leftrightarrow &-6x & = &15\\\Leftrightarrow & \color{red}{-6}x & = &15\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{15}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{+6}& = & -5 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{+6}\color{blue}{-6+3x } & = & -5 \color{red}{ -3x }\color{blue}{-6+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & -5 \color{blue}{-6} \\\Leftrightarrow &7x & = &-11\\\Leftrightarrow & \color{red}{7}x & = &-11\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-11}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{7} } & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)