Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{-12}& = & 6 \color{red}{ +3x } \\\Leftrightarrow & 4x \color{red}{-12}\color{blue}{+12-3x } & = & 6 \color{red}{ +3x }\color{blue}{+12-3x } \\\Leftrightarrow & 4x \color{blue}{-3x } & = & 6 \color{blue}{+12} \\\Leftrightarrow &x & = &18\\\Leftrightarrow & \color{red}{}x & = &18\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 18 \\\Leftrightarrow & \color{green}{ x = 18 } & & \\ & V = \left\{ 18 \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{+2}& = & 5 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{+2}\color{blue}{-2-6x } & = & 5 \color{red}{ +6x }\color{blue}{-2-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & 5 \color{blue}{-2} \\\Leftrightarrow &-11x & = &3\\\Leftrightarrow & \color{red}{-11}x & = &3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{-14}& = & 7 \color{red}{ +5x } \\\Leftrightarrow & 4x \color{red}{-14}\color{blue}{+14-5x } & = & 7 \color{red}{ +5x }\color{blue}{+14-5x } \\\Leftrightarrow & 4x \color{blue}{-5x } & = & 7 \color{blue}{+14} \\\Leftrightarrow &-x & = &21\\\Leftrightarrow & \color{red}{-}x & = &21\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{21}{-1} \\\Leftrightarrow & \color{green}{ x = -21 } & & \\ & V = \left\{ -21 \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{-2}& = & -8 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{-2}\color{blue}{+2+5x } & = & -8 \color{red}{ -5x }\color{blue}{+2+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & -8 \color{blue}{+2} \\\Leftrightarrow &11x & = &-6\\\Leftrightarrow & \color{red}{11}x & = &-6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{-5}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-5}\color{blue}{+5-x } & = & -10 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -10 \color{blue}{+5} \\\Leftrightarrow &-15x & = &-5\\\Leftrightarrow & \color{red}{-15}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{+2}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+2}\color{blue}{-2-x } & = & 8 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 8 \color{blue}{-2} \\\Leftrightarrow &13x & = &6\\\Leftrightarrow & \color{red}{13}x & = &6\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{6}{13} \\\Leftrightarrow & \color{green}{ x = \frac{6}{13} } & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{-15}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-15}\color{blue}{+15-x } & = & -10 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -10 \color{blue}{+15} \\\Leftrightarrow &x & = &5\\\Leftrightarrow & \color{red}{}x & = &5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 5 \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{-11}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-11}\color{blue}{+11-x } & = & 13 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 13 \color{blue}{+11} \\\Leftrightarrow &-10x & = &24\\\Leftrightarrow & \color{red}{-10}x & = &24\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{24}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{5} } & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{-13}& = & -2 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-13}\color{blue}{+13-9x } & = & -2 \color{red}{ +9x }\color{blue}{+13-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & -2 \color{blue}{+13} \\\Leftrightarrow &5x & = &11\\\Leftrightarrow & \color{red}{5}x & = &11\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{11}{5} \\\Leftrightarrow & \color{green}{ x = \frac{11}{5} } & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{-7}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-7}\color{blue}{+7-x } & = & 14 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 14 \color{blue}{+7} \\\Leftrightarrow &-14x & = &21\\\Leftrightarrow & \color{red}{-14}x & = &21\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{21}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{-13}& = & 5 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-13}\color{blue}{+13+11x } & = & 5 \color{red}{ -11x }\color{blue}{+13+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 5 \color{blue}{+13} \\\Leftrightarrow &23x & = &18\\\Leftrightarrow & \color{red}{23}x & = &18\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{18}{23} \\\Leftrightarrow & \color{green}{ x = \frac{18}{23} } & & \\ & V = \left\{ \frac{18}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{-15}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-15}\color{blue}{+15-x } & = & 13 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 13 \color{blue}{+15} \\\Leftrightarrow &-14x & = &28\\\Leftrightarrow & \color{red}{-14}x & = &28\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{28}{-14} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)