Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{-12}& = & -9 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{-12}\color{blue}{+12-5x } & = & -9 \color{red}{ +5x }\color{blue}{+12-5x } \\\Leftrightarrow & -2x \color{blue}{-5x } & = & -9 \color{blue}{+12} \\\Leftrightarrow &-7x & = &3\\\Leftrightarrow & \color{red}{-7}x & = &3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{+4}& = & -4 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{+4}\color{blue}{-4+9x } & = & -4 \color{red}{ -9x }\color{blue}{-4+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & -4 \color{blue}{-4} \\\Leftrightarrow &14x & = &-8\\\Leftrightarrow & \color{red}{14}x & = &-8\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-8}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{-15}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-15}\color{blue}{+15-x } & = & -8 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -8 \color{blue}{+15} \\\Leftrightarrow &-12x & = &7\\\Leftrightarrow & \color{red}{-12}x & = &7\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{7}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{12} } & & \\ & V = \left\{ \frac{-7}{12} \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{-5}& = & 3 \color{red}{ +6x } \\\Leftrightarrow & 7x \color{red}{-5}\color{blue}{+5-6x } & = & 3 \color{red}{ +6x }\color{blue}{+5-6x } \\\Leftrightarrow & 7x \color{blue}{-6x } & = & 3 \color{blue}{+5} \\\Leftrightarrow &x & = &8\\\Leftrightarrow & \color{red}{}x & = &8\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 8 \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{-1}& = & 6 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{-1}\color{blue}{+1-14x } & = & 6 \color{red}{ +14x }\color{blue}{+1-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & 6 \color{blue}{+1} \\\Leftrightarrow &-23x & = &7\\\Leftrightarrow & \color{red}{-23}x & = &7\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{7}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{23} } & & \\ & V = \left\{ \frac{-7}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{-3}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-3}\color{blue}{+3-x } & = & -13 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -13 \color{blue}{+3} \\\Leftrightarrow &13x & = &-10\\\Leftrightarrow & \color{red}{13}x & = &-10\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-10}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{13} } & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{+7}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+7}\color{blue}{-7-x } & = & -12 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -12 \color{blue}{-7} \\\Leftrightarrow &-13x & = &-19\\\Leftrightarrow & \color{red}{-13}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-19}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{19}{13} } & & \\ & V = \left\{ \frac{19}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{+11}& = & 9 \color{red}{ +7x } \\\Leftrightarrow & 13x \color{red}{+11}\color{blue}{-11-7x } & = & 9 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & 13x \color{blue}{-7x } & = & 9 \color{blue}{-11} \\\Leftrightarrow &6x & = &-2\\\Leftrightarrow & \color{red}{6}x & = &-2\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-2}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{-4}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-4}\color{blue}{+4-x } & = & 6 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 6 \color{blue}{+4} \\\Leftrightarrow &-3x & = &10\\\Leftrightarrow & \color{red}{-3}x & = &10\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{10}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{3} } & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{+14}& = & 10 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+14}\color{blue}{-14+13x } & = & 10 \color{red}{ -13x }\color{blue}{-14+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & 10 \color{blue}{-14} \\\Leftrightarrow &23x & = &-4\\\Leftrightarrow & \color{red}{23}x & = &-4\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-4}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{23} } & & \\ & V = \left\{ \frac{-4}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{-12}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-12}\color{blue}{+12-x } & = & 10 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 10 \color{blue}{+12} \\\Leftrightarrow &-13x & = &22\\\Leftrightarrow & \color{red}{-13}x & = &22\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{22}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{13} } & & \\ & V = \left\{ \frac{-22}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{+9}& = & -3 \color{red}{ +3x } \\\Leftrightarrow & 11x \color{red}{+9}\color{blue}{-9-3x } & = & -3 \color{red}{ +3x }\color{blue}{-9-3x } \\\Leftrightarrow & 11x \color{blue}{-3x } & = & -3 \color{blue}{-9} \\\Leftrightarrow &8x & = &-12\\\Leftrightarrow & \color{red}{8}x & = &-12\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-12}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)