Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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