Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{+11}& = & 1 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{+11}\color{blue}{-11-5x } & = & 1 \color{red}{ +5x }\color{blue}{-11-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & 1 \color{blue}{-11} \\\Leftrightarrow &x & = &-10\\\Leftrightarrow & \color{red}{}x & = &-10\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -10 \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{-14}& = & 14 \color{red}{ +7x } \\\Leftrightarrow & 9x \color{red}{-14}\color{blue}{+14-7x } & = & 14 \color{red}{ +7x }\color{blue}{+14-7x } \\\Leftrightarrow & 9x \color{blue}{-7x } & = & 14 \color{blue}{+14} \\\Leftrightarrow &2x & = &28\\\Leftrightarrow & \color{red}{2}x & = &28\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{28}{2} \\\Leftrightarrow & \color{green}{ x = 14 } & & \\ & V = \left\{ 14 \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{+8}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+8}\color{blue}{-8-x } & = & 6 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 6 \color{blue}{-8} \\\Leftrightarrow &-13x & = &-2\\\Leftrightarrow & \color{red}{-13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{+1}& = & 5 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{+1}\color{blue}{-1-11x } & = & 5 \color{red}{ +11x }\color{blue}{-1-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & 5 \color{blue}{-1} \\\Leftrightarrow &-21x & = &4\\\Leftrightarrow & \color{red}{-21}x & = &4\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{4}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{21} } & & \\ & V = \left\{ \frac{-4}{21} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+6}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+6}\color{blue}{-6-x } & = & 3 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 3 \color{blue}{-6} \\\Leftrightarrow &-9x & = &-3\\\Leftrightarrow & \color{red}{-9}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{+13}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+13}\color{blue}{-13-x } & = & -7 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -7 \color{blue}{-13} \\\Leftrightarrow &-11x & = &-20\\\Leftrightarrow & \color{red}{-11}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-20}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{20}{11} } & & \\ & V = \left\{ \frac{20}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{+14}& = & 14 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+14}\color{blue}{-14+11x } & = & 14 \color{red}{ -11x }\color{blue}{-14+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 14 \color{blue}{-14} \\\Leftrightarrow &23x & = &0\\\Leftrightarrow & \color{red}{23}x & = &0\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{0}{23} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{-9}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9-x } & = & -3 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -3 \color{blue}{+9} \\\Leftrightarrow &-6x & = &6\\\Leftrightarrow & \color{red}{-6}x & = &6\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{6}{-6} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{-15}& = & -3 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{-15}\color{blue}{+15+4x } & = & -3 \color{red}{ -4x }\color{blue}{+15+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -3 \color{blue}{+15} \\\Leftrightarrow &13x & = &12\\\Leftrightarrow & \color{red}{13}x & = &12\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{12}{13} \\\Leftrightarrow & \color{green}{ x = \frac{12}{13} } & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{-10}& = & -1 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{-10}\color{blue}{+10-13x } & = & -1 \color{red}{ +13x }\color{blue}{+10-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & -1 \color{blue}{+10} \\\Leftrightarrow &-17x & = &9\\\Leftrightarrow & \color{red}{-17}x & = &9\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{9}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{17} } & & \\ & V = \left\{ \frac{-9}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{-12}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & 4x \color{red}{-12}\color{blue}{+12-13x } & = & 9 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & 4x \color{blue}{-13x } & = & 9 \color{blue}{+12} \\\Leftrightarrow &-9x & = &21\\\Leftrightarrow & \color{red}{-9}x & = &21\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{21}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{+1}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+1}\color{blue}{-1-x } & = & -3 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -3 \color{blue}{-1} \\\Leftrightarrow &-15x & = &-4\\\Leftrightarrow & \color{red}{-15}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{15} } & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)