Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{-14}& = & 6 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{-14}\color{blue}{+14-14x } & = & 6 \color{red}{ +14x }\color{blue}{+14-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & 6 \color{blue}{+14} \\\Leftrightarrow &-23x & = &20\\\Leftrightarrow & \color{red}{-23}x & = &20\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{20}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{23} } & & \\ & V = \left\{ \frac{-20}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{-9}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-9}\color{blue}{+9-x } & = & 3 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 3 \color{blue}{+9} \\\Leftrightarrow &-12x & = &12\\\Leftrightarrow & \color{red}{-12}x & = &12\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{12}{-12} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{+8}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+8}\color{blue}{-8-x } & = & -7 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -7 \color{blue}{-8} \\\Leftrightarrow &-13x & = &-15\\\Leftrightarrow & \color{red}{-13}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-15}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{15}{13} } & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{+8}& = & 2 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{+8}\color{blue}{-8+11x } & = & 2 \color{red}{ -11x }\color{blue}{-8+11x } \\\Leftrightarrow & 9x \color{blue}{+11x } & = & 2 \color{blue}{-8} \\\Leftrightarrow &20x & = &-6\\\Leftrightarrow & \color{red}{20}x & = &-6\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-6}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{10} } & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{-8}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-8}\color{blue}{+8-x } & = & -6 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -6 \color{blue}{+8} \\\Leftrightarrow &-12x & = &2\\\Leftrightarrow & \color{red}{-12}x & = &2\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{2}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{-3}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-3}\color{blue}{+3-x } & = & -10 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -10 \color{blue}{+3} \\\Leftrightarrow &-7x & = &-7\\\Leftrightarrow & \color{red}{-7}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-7}{-7} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{-15}& = & -15 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{-15}\color{blue}{+15-13x } & = & -15 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & -15 \color{blue}{+15} \\\Leftrightarrow &-3x & = &0\\\Leftrightarrow & \color{red}{-3}x & = &0\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{0}{-3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{+9}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+9}\color{blue}{-9-x } & = & 7 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 7 \color{blue}{-9} \\\Leftrightarrow &11x & = &-2\\\Leftrightarrow & \color{red}{11}x & = &-2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{+11}& = & -5 \color{red}{ +6x } \\\Leftrightarrow & 5x \color{red}{+11}\color{blue}{-11-6x } & = & -5 \color{red}{ +6x }\color{blue}{-11-6x } \\\Leftrightarrow & 5x \color{blue}{-6x } & = & -5 \color{blue}{-11} \\\Leftrightarrow &-x & = &-16\\\Leftrightarrow & \color{red}{-}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-16}{-1} \\\Leftrightarrow & \color{green}{ x = 16 } & & \\ & V = \left\{ 16 \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{-6}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{-6}\color{blue}{+6-13x } & = & -7 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & 12x \color{blue}{-13x } & = & -7 \color{blue}{+6} \\\Leftrightarrow &-x & = &-1\\\Leftrightarrow & \color{red}{-}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-1}{-1} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{-6}& = & -10 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-6}\color{blue}{+6-7x } & = & -10 \color{red}{ +7x }\color{blue}{+6-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -10 \color{blue}{+6} \\\Leftrightarrow &-13x & = &-4\\\Leftrightarrow & \color{red}{-13}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{+12}& = & 8 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+12}\color{blue}{-12+5x } & = & 8 \color{red}{ -5x }\color{blue}{-12+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 8 \color{blue}{-12} \\\Leftrightarrow &11x & = &-4\\\Leftrightarrow & \color{red}{11}x & = &-4\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-4}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)