Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{-14}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-14}\color{blue}{+14-x } & = & 7 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 7 \color{blue}{+14} \\\Leftrightarrow &-9x & = &21\\\Leftrightarrow & \color{red}{-9}x & = &21\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{21}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{+7}& = & -1 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+7}\color{blue}{-7-5x } & = & -1 \color{red}{ +5x }\color{blue}{-7-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -1 \color{blue}{-7} \\\Leftrightarrow &7x & = &-8\\\Leftrightarrow & \color{red}{7}x & = &-8\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-8}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{-3}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-3}\color{blue}{+3-x } & = & -3 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -3 \color{blue}{+3} \\\Leftrightarrow &x & = &0\\\Leftrightarrow & \color{red}{}x & = &0\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 0 \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{-11}& = & 3 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{-11}\color{blue}{+11+3x } & = & 3 \color{red}{ -3x }\color{blue}{+11+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & 3 \color{blue}{+11} \\\Leftrightarrow &10x & = &14\\\Leftrightarrow & \color{red}{10}x & = &14\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{14}{10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{+2}& = & 9 \color{red}{ +2x } \\\Leftrightarrow & 9x \color{red}{+2}\color{blue}{-2-2x } & = & 9 \color{red}{ +2x }\color{blue}{-2-2x } \\\Leftrightarrow & 9x \color{blue}{-2x } & = & 9 \color{blue}{-2} \\\Leftrightarrow &7x & = &7\\\Leftrightarrow & \color{red}{7}x & = &7\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{7}{7} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{+12}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & 2x \color{red}{+12}\color{blue}{-12-13x } & = & 9 \color{red}{ +13x }\color{blue}{-12-13x } \\\Leftrightarrow & 2x \color{blue}{-13x } & = & 9 \color{blue}{-12} \\\Leftrightarrow &-11x & = &-3\\\Leftrightarrow & \color{red}{-11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{-11}& = & 9 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-11}\color{blue}{+11-9x } & = & 9 \color{red}{ +9x }\color{blue}{+11-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & 9 \color{blue}{+11} \\\Leftrightarrow &-13x & = &20\\\Leftrightarrow & \color{red}{-13}x & = &20\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{20}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{13} } & & \\ & V = \left\{ \frac{-20}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{-3}& = & 7 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{-3}\color{blue}{+3-11x } & = & 7 \color{red}{ +11x }\color{blue}{+3-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & 7 \color{blue}{+3} \\\Leftrightarrow &-5x & = &10\\\Leftrightarrow & \color{red}{-5}x & = &10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{10}{-5} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{+15}& = & -9 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{+15}\color{blue}{-15-13x } & = & -9 \color{red}{ +13x }\color{blue}{-15-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & -9 \color{blue}{-15} \\\Leftrightarrow &-17x & = &-24\\\Leftrightarrow & \color{red}{-17}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-24}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{24}{17} } & & \\ & V = \left\{ \frac{24}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{+5}& = & -11 \color{red}{ +11x } \\\Leftrightarrow & 14x \color{red}{+5}\color{blue}{-5-11x } & = & -11 \color{red}{ +11x }\color{blue}{-5-11x } \\\Leftrightarrow & 14x \color{blue}{-11x } & = & -11 \color{blue}{-5} \\\Leftrightarrow &3x & = &-16\\\Leftrightarrow & \color{red}{3}x & = &-16\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-16}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{3} } & & \\ & V = \left\{ \frac{-16}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{-6}& = & -15 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{-6}\color{blue}{+6-5x } & = & -15 \color{red}{ +5x }\color{blue}{+6-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & -15 \color{blue}{+6} \\\Leftrightarrow &-14x & = &-9\\\Leftrightarrow & \color{red}{-14}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-9}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{9}{14} } & & \\ & V = \left\{ \frac{9}{14} \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{-15}& = & -15 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-15}\color{blue}{+15-7x } & = & -15 \color{red}{ +7x }\color{blue}{+15-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -15 \color{blue}{+15} \\\Leftrightarrow &-17x & = &0\\\Leftrightarrow & \color{red}{-17}x & = &0\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{0}{-17} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)