Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{+4}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+4}\color{blue}{-4-x } & = & 1 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 1 \color{blue}{-4} \\\Leftrightarrow &-12x & = &-3\\\Leftrightarrow & \color{red}{-12}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-3}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{-5}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-5}\color{blue}{+5-x } & = & -8 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -8 \color{blue}{+5} \\\Leftrightarrow &-13x & = &-3\\\Leftrightarrow & \color{red}{-13}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{3}{13} } & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{-14}& = & -11 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{-14}\color{blue}{+14+5x } & = & -11 \color{red}{ -5x }\color{blue}{+14+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & -11 \color{blue}{+14} \\\Leftrightarrow &8x & = &3\\\Leftrightarrow & \color{red}{8}x & = &3\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{3}{8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{-11}& = & -1 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-11}\color{blue}{+11+8x } & = & -1 \color{red}{ -8x }\color{blue}{+11+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & -1 \color{blue}{+11} \\\Leftrightarrow &11x & = &10\\\Leftrightarrow & \color{red}{11}x & = &10\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{10}{11} \\\Leftrightarrow & \color{green}{ x = \frac{10}{11} } & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{+15}& = & 1 \color{red}{ +9x } \\\Leftrightarrow & 13x \color{red}{+15}\color{blue}{-15-9x } & = & 1 \color{red}{ +9x }\color{blue}{-15-9x } \\\Leftrightarrow & 13x \color{blue}{-9x } & = & 1 \color{blue}{-15} \\\Leftrightarrow &4x & = &-14\\\Leftrightarrow & \color{red}{4}x & = &-14\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-14}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{-13}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & 11x \color{red}{-13}\color{blue}{+13-13x } & = & 13 \color{red}{ +13x }\color{blue}{+13-13x } \\\Leftrightarrow & 11x \color{blue}{-13x } & = & 13 \color{blue}{+13} \\\Leftrightarrow &-2x & = &26\\\Leftrightarrow & \color{red}{-2}x & = &26\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{26}{-2} \\\Leftrightarrow & \color{green}{ x = -13 } & & \\ & V = \left\{ -13 \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{-4}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-4}\color{blue}{+4-x } & = & -3 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -3 \color{blue}{+4} \\\Leftrightarrow &-9x & = &1\\\Leftrightarrow & \color{red}{-9}x & = &1\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{1}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{9} } & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{-2}& = & -2 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{-2}\color{blue}{+2-14x } & = & -2 \color{red}{ +14x }\color{blue}{+2-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -2 \color{blue}{+2} \\\Leftrightarrow &-23x & = &0\\\Leftrightarrow & \color{red}{-23}x & = &0\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{0}{-23} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{+7}& = & -12 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+7}\color{blue}{-7+7x } & = & -12 \color{red}{ -7x }\color{blue}{-7+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -12 \color{blue}{-7} \\\Leftrightarrow &15x & = &-19\\\Leftrightarrow & \color{red}{15}x & = &-19\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-19}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{15} } & & \\ & V = \left\{ \frac{-19}{15} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{-6}& = & 13 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-6}\color{blue}{+6+13x } & = & 13 \color{red}{ -13x }\color{blue}{+6+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & 13 \color{blue}{+6} \\\Leftrightarrow &23x & = &19\\\Leftrightarrow & \color{red}{23}x & = &19\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{19}{23} \\\Leftrightarrow & \color{green}{ x = \frac{19}{23} } & & \\ & V = \left\{ \frac{19}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{-9}& = & -13 \color{red}{ +10x } \\\Leftrightarrow & 3x \color{red}{-9}\color{blue}{+9-10x } & = & -13 \color{red}{ +10x }\color{blue}{+9-10x } \\\Leftrightarrow & 3x \color{blue}{-10x } & = & -13 \color{blue}{+9} \\\Leftrightarrow &-7x & = &-4\\\Leftrightarrow & \color{red}{-7}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{+2}& = & 14 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+2}\color{blue}{-2-x } & = & 14 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 14 \color{blue}{-2} \\\Leftrightarrow &13x & = &12\\\Leftrightarrow & \color{red}{13}x & = &12\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{12}{13} \\\Leftrightarrow & \color{green}{ x = \frac{12}{13} } & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)