Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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