Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{-11}& = & -8 \color{red}{ +3x } \\\Leftrightarrow & -11x \color{red}{-11}\color{blue}{+11-3x } & = & -8 \color{red}{ +3x }\color{blue}{+11-3x } \\\Leftrightarrow & -11x \color{blue}{-3x } & = & -8 \color{blue}{+11} \\\Leftrightarrow &-14x & = &3\\\Leftrightarrow & \color{red}{-14}x & = &3\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{3}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{14} } & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{+2}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+2}\color{blue}{-2-x } & = & 6 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 6 \color{blue}{-2} \\\Leftrightarrow &-15x & = &4\\\Leftrightarrow & \color{red}{-15}x & = &4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{15} } & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{+5}& = & 1 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+5}\color{blue}{-5-5x } & = & 1 \color{red}{ +5x }\color{blue}{-5-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & 1 \color{blue}{-5} \\\Leftrightarrow &-9x & = &-4\\\Leftrightarrow & \color{red}{-9}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-4}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{9} } & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{-14}& = & 2 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-14}\color{blue}{+14-14x } & = & 2 \color{red}{ +14x }\color{blue}{+14-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & 2 \color{blue}{+14} \\\Leftrightarrow &-27x & = &16\\\Leftrightarrow & \color{red}{-27}x & = &16\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{16}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{27} } & & \\ & V = \left\{ \frac{-16}{27} \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{+9}& = & -15 \color{red}{ -3x } \\\Leftrightarrow & x \color{red}{+9}\color{blue}{-9+3x } & = & -15 \color{red}{ -3x }\color{blue}{-9+3x } \\\Leftrightarrow & x \color{blue}{+3x } & = & -15 \color{blue}{-9} \\\Leftrightarrow &4x & = &-24\\\Leftrightarrow & \color{red}{4}x & = &-24\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-24}{4} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{-13}& = & -13 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{-13}\color{blue}{+13-8x } & = & -13 \color{red}{ +8x }\color{blue}{+13-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & -13 \color{blue}{+13} \\\Leftrightarrow &-23x & = &0\\\Leftrightarrow & \color{red}{-23}x & = &0\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{0}{-23} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{+5}& = & -14 \color{red}{ +6x } \\\Leftrightarrow & x \color{red}{+5}\color{blue}{-5-6x } & = & -14 \color{red}{ +6x }\color{blue}{-5-6x } \\\Leftrightarrow & x \color{blue}{-6x } & = & -14 \color{blue}{-5} \\\Leftrightarrow &-5x & = &-19\\\Leftrightarrow & \color{red}{-5}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-19}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{19}{5} } & & \\ & V = \left\{ \frac{19}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{+7}& = & -10 \color{red}{ +9x } \\\Leftrightarrow & 2x \color{red}{+7}\color{blue}{-7-9x } & = & -10 \color{red}{ +9x }\color{blue}{-7-9x } \\\Leftrightarrow & 2x \color{blue}{-9x } & = & -10 \color{blue}{-7} \\\Leftrightarrow &-7x & = &-17\\\Leftrightarrow & \color{red}{-7}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-17}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{17}{7} } & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{+6}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+6}\color{blue}{-6-x } & = & 1 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 1 \color{blue}{-6} \\\Leftrightarrow &-8x & = &-5\\\Leftrightarrow & \color{red}{-8}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-5}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{+14}& = & 1 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{+14}\color{blue}{-14+2x } & = & 1 \color{red}{ -2x }\color{blue}{-14+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & 1 \color{blue}{-14} \\\Leftrightarrow &13x & = &-13\\\Leftrightarrow & \color{red}{13}x & = &-13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-13}{13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{+6}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+6}\color{blue}{-6-x } & = & -14 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -14 \color{blue}{-6} \\\Leftrightarrow &-13x & = &-20\\\Leftrightarrow & \color{red}{-13}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-20}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{20}{13} } & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{+9}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+9}\color{blue}{-9-x } & = & -1 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -1 \color{blue}{-9} \\\Leftrightarrow &-8x & = &-10\\\Leftrightarrow & \color{red}{-8}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-10}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)