Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{+8}& = & -11 \color{red}{ +14x } \\\Leftrightarrow & 3x \color{red}{+8}\color{blue}{-8-14x } & = & -11 \color{red}{ +14x }\color{blue}{-8-14x } \\\Leftrightarrow & 3x \color{blue}{-14x } & = & -11 \color{blue}{-8} \\\Leftrightarrow &-11x & = &-19\\\Leftrightarrow & \color{red}{-11}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-19}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{19}{11} } & & \\ & V = \left\{ \frac{19}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{-6}& = & 12 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{-6}\color{blue}{+6-8x } & = & 12 \color{red}{ +8x }\color{blue}{+6-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & 12 \color{blue}{+6} \\\Leftrightarrow &-15x & = &18\\\Leftrightarrow & \color{red}{-15}x & = &18\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{18}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{-6}& = & 4 \color{red}{ +13x } \\\Leftrightarrow & 8x \color{red}{-6}\color{blue}{+6-13x } & = & 4 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & 8x \color{blue}{-13x } & = & 4 \color{blue}{+6} \\\Leftrightarrow &-5x & = &10\\\Leftrightarrow & \color{red}{-5}x & = &10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{10}{-5} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{+15}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+15}\color{blue}{-15-x } & = & 14 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 14 \color{blue}{-15} \\\Leftrightarrow &-4x & = &-1\\\Leftrightarrow & \color{red}{-4}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{+8}& = & -1 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+8}\color{blue}{-8+11x } & = & -1 \color{red}{ -11x }\color{blue}{-8+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -1 \color{blue}{-8} \\\Leftrightarrow &17x & = &-9\\\Leftrightarrow & \color{red}{17}x & = &-9\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-9}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{17} } & & \\ & V = \left\{ \frac{-9}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{+3}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{+3}\color{blue}{-3-x } & = & -12 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & -12 \color{blue}{-3} \\\Leftrightarrow &2x & = &-15\\\Leftrightarrow & \color{red}{2}x & = &-15\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-15}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{2} } & & \\ & V = \left\{ \frac{-15}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{-6}& = & -12 \color{red}{ -13x } \\\Leftrightarrow & 8x \color{red}{-6}\color{blue}{+6+13x } & = & -12 \color{red}{ -13x }\color{blue}{+6+13x } \\\Leftrightarrow & 8x \color{blue}{+13x } & = & -12 \color{blue}{+6} \\\Leftrightarrow &21x & = &-6\\\Leftrightarrow & \color{red}{21}x & = &-6\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-6}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{+14}& = & 14 \color{red}{ +2x } \\\Leftrightarrow & -x \color{red}{+14}\color{blue}{-14-2x } & = & 14 \color{red}{ +2x }\color{blue}{-14-2x } \\\Leftrightarrow & -x \color{blue}{-2x } & = & 14 \color{blue}{-14} \\\Leftrightarrow &-3x & = &0\\\Leftrightarrow & \color{red}{-3}x & = &0\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{0}{-3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{-15}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-15}\color{blue}{+15-x } & = & 7 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 7 \color{blue}{+15} \\\Leftrightarrow &-16x & = &22\\\Leftrightarrow & \color{red}{-16}x & = &22\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{22}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{8} } & & \\ & V = \left\{ \frac{-11}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{-6}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-6}\color{blue}{+6-x } & = & 1 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 1 \color{blue}{+6} \\\Leftrightarrow &-9x & = &7\\\Leftrightarrow & \color{red}{-9}x & = &7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{9} } & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{+14}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+14}\color{blue}{-14-x } & = & 4 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 4 \color{blue}{-14} \\\Leftrightarrow &-16x & = &-10\\\Leftrightarrow & \color{red}{-16}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-10}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{+3}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+3}\color{blue}{-3-x } & = & -5 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -5 \color{blue}{-3} \\\Leftrightarrow &-15x & = &-8\\\Leftrightarrow & \color{red}{-15}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{8}{15} } & & \\ & V = \left\{ \frac{8}{15} \right\} & \\\end{align}\)