Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{+8}& = & 15 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+8}\color{blue}{-8+11x } & = & 15 \color{red}{ -11x }\color{blue}{-8+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 15 \color{blue}{-8} \\\Leftrightarrow &17x & = &7\\\Leftrightarrow & \color{red}{17}x & = &7\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{7}{17} \\\Leftrightarrow & \color{green}{ x = \frac{7}{17} } & & \\ & V = \left\{ \frac{7}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{+2}& = & 6 \color{red}{ -14x } \\\Leftrightarrow & x \color{red}{+2}\color{blue}{-2+14x } & = & 6 \color{red}{ -14x }\color{blue}{-2+14x } \\\Leftrightarrow & x \color{blue}{+14x } & = & 6 \color{blue}{-2} \\\Leftrightarrow &15x & = &4\\\Leftrightarrow & \color{red}{15}x & = &4\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{4}{15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{15} } & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{-6}& = & -11 \color{red}{ +13x } \\\Leftrightarrow & 11x \color{red}{-6}\color{blue}{+6-13x } & = & -11 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & 11x \color{blue}{-13x } & = & -11 \color{blue}{+6} \\\Leftrightarrow &-2x & = &-5\\\Leftrightarrow & \color{red}{-2}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-5}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{+15}& = & 9 \color{red}{ -13x } \\\Leftrightarrow & 8x \color{red}{+15}\color{blue}{-15+13x } & = & 9 \color{red}{ -13x }\color{blue}{-15+13x } \\\Leftrightarrow & 8x \color{blue}{+13x } & = & 9 \color{blue}{-15} \\\Leftrightarrow &21x & = &-6\\\Leftrightarrow & \color{red}{21}x & = &-6\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-6}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{-4}& = & 15 \color{red}{ +2x } \\\Leftrightarrow & -x \color{red}{-4}\color{blue}{+4-2x } & = & 15 \color{red}{ +2x }\color{blue}{+4-2x } \\\Leftrightarrow & -x \color{blue}{-2x } & = & 15 \color{blue}{+4} \\\Leftrightarrow &-3x & = &19\\\Leftrightarrow & \color{red}{-3}x & = &19\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{19}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{3} } & & \\ & V = \left\{ \frac{-19}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{-11}& = & -6 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{-11}\color{blue}{+11-6x } & = & -6 \color{red}{ +6x }\color{blue}{+11-6x } \\\Leftrightarrow & -11x \color{blue}{-6x } & = & -6 \color{blue}{+11} \\\Leftrightarrow &-17x & = &5\\\Leftrightarrow & \color{red}{-17}x & = &5\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{5}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{17} } & & \\ & V = \left\{ \frac{-5}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{+15}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+15}\color{blue}{-15-13x } & = & 14 \color{red}{ +13x }\color{blue}{-15-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 14 \color{blue}{-15} \\\Leftrightarrow &-19x & = &-1\\\Leftrightarrow & \color{red}{-19}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-1}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{1}{19} } & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{-13}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-13}\color{blue}{+13-x } & = & -4 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -4 \color{blue}{+13} \\\Leftrightarrow &-15x & = &9\\\Leftrightarrow & \color{red}{-15}x & = &9\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{9}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{-12}& = & -15 \color{red}{ +11x } \\\Leftrightarrow & 5x \color{red}{-12}\color{blue}{+12-11x } & = & -15 \color{red}{ +11x }\color{blue}{+12-11x } \\\Leftrightarrow & 5x \color{blue}{-11x } & = & -15 \color{blue}{+12} \\\Leftrightarrow &-6x & = &-3\\\Leftrightarrow & \color{red}{-6}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-3}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{-8}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8-x } & = & -13 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -13 \color{blue}{+8} \\\Leftrightarrow &13x & = &-5\\\Leftrightarrow & \color{red}{13}x & = &-5\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-5}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{-1}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-1}\color{blue}{+1-x } & = & -6 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -6 \color{blue}{+1} \\\Leftrightarrow &-16x & = &-5\\\Leftrightarrow & \color{red}{-16}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-5}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{16} } & & \\ & V = \left\{ \frac{5}{16} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{+3}& = & -4 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+3}\color{blue}{-3+11x } & = & -4 \color{red}{ -11x }\color{blue}{-3+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -4 \color{blue}{-3} \\\Leftrightarrow &17x & = &-7\\\Leftrightarrow & \color{red}{17}x & = &-7\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-7}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{17} } & & \\ & V = \left\{ \frac{-7}{17} \right\} & \\\end{align}\)