Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{+6}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+6}\color{blue}{-6-x } & = & 14 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 14 \color{blue}{-6} \\\Leftrightarrow &-10x & = &8\\\Leftrightarrow & \color{red}{-10}x & = &8\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{8}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{-9}& = & 3 \color{red}{ -13x } \\\Leftrightarrow & 8x \color{red}{-9}\color{blue}{+9+13x } & = & 3 \color{red}{ -13x }\color{blue}{+9+13x } \\\Leftrightarrow & 8x \color{blue}{+13x } & = & 3 \color{blue}{+9} \\\Leftrightarrow &21x & = &12\\\Leftrightarrow & \color{red}{21}x & = &12\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{12}{21} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{+6}& = & 5 \color{red}{ +11x } \\\Leftrightarrow & 10x \color{red}{+6}\color{blue}{-6-11x } & = & 5 \color{red}{ +11x }\color{blue}{-6-11x } \\\Leftrightarrow & 10x \color{blue}{-11x } & = & 5 \color{blue}{-6} \\\Leftrightarrow &-x & = &-1\\\Leftrightarrow & \color{red}{-}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-1}{-1} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{+13}& = & -5 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+13}\color{blue}{-13+11x } & = & -5 \color{red}{ -11x }\color{blue}{-13+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & -5 \color{blue}{-13} \\\Leftrightarrow &15x & = &-18\\\Leftrightarrow & \color{red}{15}x & = &-18\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-18}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{-15}& = & 2 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{-15}\color{blue}{+15+5x } & = & 2 \color{red}{ -5x }\color{blue}{+15+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 2 \color{blue}{+15} \\\Leftrightarrow &11x & = &17\\\Leftrightarrow & \color{red}{11}x & = &17\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{17}{11} \\\Leftrightarrow & \color{green}{ x = \frac{17}{11} } & & \\ & V = \left\{ \frac{17}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{+8}& = & -3 \color{red}{ -5x } \\\Leftrightarrow & 8x \color{red}{+8}\color{blue}{-8+5x } & = & -3 \color{red}{ -5x }\color{blue}{-8+5x } \\\Leftrightarrow & 8x \color{blue}{+5x } & = & -3 \color{blue}{-8} \\\Leftrightarrow &13x & = &-11\\\Leftrightarrow & \color{red}{13}x & = &-11\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-11}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{13} } & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{+14}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+14}\color{blue}{-14-x } & = & 2 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 2 \color{blue}{-14} \\\Leftrightarrow &-7x & = &-12\\\Leftrightarrow & \color{red}{-7}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-12}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{12}{7} } & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{-6}& = & 12 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-6}\color{blue}{+6-14x } & = & 12 \color{red}{ +14x }\color{blue}{+6-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & 12 \color{blue}{+6} \\\Leftrightarrow &-27x & = &18\\\Leftrightarrow & \color{red}{-27}x & = &18\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{18}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{-6}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-6}\color{blue}{+6-x } & = & -3 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -3 \color{blue}{+6} \\\Leftrightarrow &-7x & = &3\\\Leftrightarrow & \color{red}{-7}x & = &3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{+2}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+2}\color{blue}{-2-x } & = & -6 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -6 \color{blue}{-2} \\\Leftrightarrow &-15x & = &-8\\\Leftrightarrow & \color{red}{-15}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{8}{15} } & & \\ & V = \left\{ \frac{8}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & 2x \color{red}{+7}& = & 2 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{+7}\color{blue}{-7-3x } & = & 2 \color{red}{ +3x }\color{blue}{-7-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & 2 \color{blue}{-7} \\\Leftrightarrow &-x & = &-5\\\Leftrightarrow & \color{red}{-}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-5}{-1} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{+6}& = & -13 \color{red}{ +13x } \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6-13x } & = & -13 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & 15x \color{blue}{-13x } & = & -13 \color{blue}{-6} \\\Leftrightarrow &2x & = &-19\\\Leftrightarrow & \color{red}{2}x & = &-19\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-19}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{2} } & & \\ & V = \left\{ \frac{-19}{2} \right\} & \\\end{align}\)