Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{-11}& = & -14 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-11}\color{blue}{+11-7x } & = & -14 \color{red}{ +7x }\color{blue}{+11-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -14 \color{blue}{+11} \\\Leftrightarrow &-13x & = &-3\\\Leftrightarrow & \color{red}{-13}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{3}{13} } & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{-14}& = & 14 \color{red}{ +5x } \\\Leftrightarrow & 4x \color{red}{-14}\color{blue}{+14-5x } & = & 14 \color{red}{ +5x }\color{blue}{+14-5x } \\\Leftrightarrow & 4x \color{blue}{-5x } & = & 14 \color{blue}{+14} \\\Leftrightarrow &-x & = &28\\\Leftrightarrow & \color{red}{-}x & = &28\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{28}{-1} \\\Leftrightarrow & \color{green}{ x = -28 } & & \\ & V = \left\{ -28 \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{+15}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{+15}\color{blue}{-15-x } & = & 6 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & 6 \color{blue}{-15} \\\Leftrightarrow &12x & = &-9\\\Leftrightarrow & \color{red}{12}x & = &-9\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-9}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{-5}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & -x \color{red}{-5}\color{blue}{+5-13x } & = & 9 \color{red}{ +13x }\color{blue}{+5-13x } \\\Leftrightarrow & -x \color{blue}{-13x } & = & 9 \color{blue}{+5} \\\Leftrightarrow &-14x & = &14\\\Leftrightarrow & \color{red}{-14}x & = &14\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{14}{-14} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{-15}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-15}\color{blue}{+15-x } & = & -13 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -13 \color{blue}{+15} \\\Leftrightarrow &5x & = &2\\\Leftrightarrow & \color{red}{5}x & = &2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{+8}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+8}\color{blue}{-8-x } & = & 7 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 7 \color{blue}{-8} \\\Leftrightarrow &-10x & = &-1\\\Leftrightarrow & \color{red}{-10}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{10} } & & \\ & V = \left\{ \frac{1}{10} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{+5}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+5}\color{blue}{-5-x } & = & 10 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 10 \color{blue}{-5} \\\Leftrightarrow &-15x & = &5\\\Leftrightarrow & \color{red}{-15}x & = &5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{+14}& = & -14 \color{red}{ +5x } \\\Leftrightarrow & 2x \color{red}{+14}\color{blue}{-14-5x } & = & -14 \color{red}{ +5x }\color{blue}{-14-5x } \\\Leftrightarrow & 2x \color{blue}{-5x } & = & -14 \color{blue}{-14} \\\Leftrightarrow &-3x & = &-28\\\Leftrightarrow & \color{red}{-3}x & = &-28\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-28}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{28}{3} } & & \\ & V = \left\{ \frac{28}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{+7}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+7}\color{blue}{-7-x } & = & 9 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & 9 \color{blue}{-7} \\\Leftrightarrow &9x & = &2\\\Leftrightarrow & \color{red}{9}x & = &2\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{2}{9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{9} } & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{-11}& = & -1 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{-11}\color{blue}{+11+8x } & = & -1 \color{red}{ -8x }\color{blue}{+11+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & -1 \color{blue}{+11} \\\Leftrightarrow &17x & = &10\\\Leftrightarrow & \color{red}{17}x & = &10\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{10}{17} \\\Leftrightarrow & \color{green}{ x = \frac{10}{17} } & & \\ & V = \left\{ \frac{10}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{-10}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-10}\color{blue}{+10-x } & = & -11 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -11 \color{blue}{+10} \\\Leftrightarrow &-4x & = &-1\\\Leftrightarrow & \color{red}{-4}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{+6}& = & 1 \color{red}{ +8x } \\\Leftrightarrow & 11x \color{red}{+6}\color{blue}{-6-8x } & = & 1 \color{red}{ +8x }\color{blue}{-6-8x } \\\Leftrightarrow & 11x \color{blue}{-8x } & = & 1 \color{blue}{-6} \\\Leftrightarrow &3x & = &-5\\\Leftrightarrow & \color{red}{3}x & = &-5\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-5}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)