Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{-12}& = & 12 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{-12}\color{blue}{+12+14x } & = & 12 \color{red}{ -14x }\color{blue}{+12+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & 12 \color{blue}{+12} \\\Leftrightarrow &29x & = &24\\\Leftrightarrow & \color{red}{29}x & = &24\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{24}{29} \\\Leftrightarrow & \color{green}{ x = \frac{24}{29} } & & \\ & V = \left\{ \frac{24}{29} \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{+3}& = & 2 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{+3}\color{blue}{-3+14x } & = & 2 \color{red}{ -14x }\color{blue}{-3+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & 2 \color{blue}{-3} \\\Leftrightarrow &19x & = &-1\\\Leftrightarrow & \color{red}{19}x & = &-1\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-1}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{19} } & & \\ & V = \left\{ \frac{-1}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{-8}& = & -3 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{-8}\color{blue}{+8-3x } & = & -3 \color{red}{ +3x }\color{blue}{+8-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & -3 \color{blue}{+8} \\\Leftrightarrow &-8x & = &5\\\Leftrightarrow & \color{red}{-8}x & = &5\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{5}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{+11}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+11}\color{blue}{-11-x } & = & 4 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 4 \color{blue}{-11} \\\Leftrightarrow &-6x & = &-7\\\Leftrightarrow & \color{red}{-6}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-7}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{6} } & & \\ & V = \left\{ \frac{7}{6} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{+13}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{+13}\color{blue}{-13-13x } & = & 13 \color{red}{ +13x }\color{blue}{-13-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & 13 \color{blue}{-13} \\\Leftrightarrow &-16x & = &0\\\Leftrightarrow & \color{red}{-16}x & = &0\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{0}{-16} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{-13}& = & -14 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-13}\color{blue}{+13-9x } & = & -14 \color{red}{ +9x }\color{blue}{+13-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -14 \color{blue}{+13} \\\Leftrightarrow &-17x & = &-1\\\Leftrightarrow & \color{red}{-17}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-1}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{1}{17} } & & \\ & V = \left\{ \frac{1}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{-5}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-5}\color{blue}{+5-x } & = & -5 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -5 \color{blue}{+5} \\\Leftrightarrow &-7x & = &0\\\Leftrightarrow & \color{red}{-7}x & = &0\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{0}{-7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{-8}& = & 2 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{-8}\color{blue}{+8+2x } & = & 2 \color{red}{ -2x }\color{blue}{+8+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & 2 \color{blue}{+8} \\\Leftrightarrow &5x & = &10\\\Leftrightarrow & \color{red}{5}x & = &10\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{10}{5} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{+2}& = & 10 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+2}\color{blue}{-2-7x } & = & 10 \color{red}{ +7x }\color{blue}{-2-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 10 \color{blue}{-2} \\\Leftrightarrow &3x & = &8\\\Leftrightarrow & \color{red}{3}x & = &8\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{8}{3} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{+7}& = & -2 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{+7}\color{blue}{-7+11x } & = & -2 \color{red}{ -11x }\color{blue}{-7+11x } \\\Leftrightarrow & 14x \color{blue}{+11x } & = & -2 \color{blue}{-7} \\\Leftrightarrow &25x & = &-9\\\Leftrightarrow & \color{red}{25}x & = &-9\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-9}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{25} } & & \\ & V = \left\{ \frac{-9}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{-14}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-14}\color{blue}{+14-x } & = & 8 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 8 \color{blue}{+14} \\\Leftrightarrow &5x & = &22\\\Leftrightarrow & \color{red}{5}x & = &22\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{22}{5} \\\Leftrightarrow & \color{green}{ x = \frac{22}{5} } & & \\ & V = \left\{ \frac{22}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{+15}& = & 1 \color{red}{ +6x } \\\Leftrightarrow & -x \color{red}{+15}\color{blue}{-15-6x } & = & 1 \color{red}{ +6x }\color{blue}{-15-6x } \\\Leftrightarrow & -x \color{blue}{-6x } & = & 1 \color{blue}{-15} \\\Leftrightarrow &-7x & = &-14\\\Leftrightarrow & \color{red}{-7}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-14}{-7} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)