Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{-3}& = & -15 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-3}\color{blue}{+3+11x } & = & -15 \color{red}{ -11x }\color{blue}{+3+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -15 \color{blue}{+3} \\\Leftrightarrow &23x & = &-12\\\Leftrightarrow & \color{red}{23}x & = &-12\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-12}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{23} } & & \\ & V = \left\{ \frac{-12}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{-2}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-2}\color{blue}{+2-x } & = & 8 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 8 \color{blue}{+2} \\\Leftrightarrow &-11x & = &10\\\Leftrightarrow & \color{red}{-11}x & = &10\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{10}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{11} } & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{+3}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+3}\color{blue}{-3-x } & = & 13 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 13 \color{blue}{-3} \\\Leftrightarrow &11x & = &10\\\Leftrightarrow & \color{red}{11}x & = &10\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{10}{11} \\\Leftrightarrow & \color{green}{ x = \frac{10}{11} } & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{-6}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-6}\color{blue}{+6-x } & = & 10 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 10 \color{blue}{+6} \\\Leftrightarrow &x & = &16\\\Leftrightarrow & \color{red}{}x & = &16\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 16 \\\Leftrightarrow & \color{green}{ x = 16 } & & \\ & V = \left\{ 16 \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{-5}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-5}\color{blue}{+5-x } & = & 2 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 2 \color{blue}{+5} \\\Leftrightarrow &-13x & = &7\\\Leftrightarrow & \color{red}{-13}x & = &7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{13} } & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{+4}& = & 3 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{+4}\color{blue}{-4+2x } & = & 3 \color{red}{ -2x }\color{blue}{-4+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & 3 \color{blue}{-4} \\\Leftrightarrow &13x & = &-1\\\Leftrightarrow & \color{red}{13}x & = &-1\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-1}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{-6}& = & -9 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-6}\color{blue}{+6-7x } & = & -9 \color{red}{ +7x }\color{blue}{+6-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -9 \color{blue}{+6} \\\Leftrightarrow &-13x & = &-3\\\Leftrightarrow & \color{red}{-13}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{3}{13} } & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{+6}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+6}\color{blue}{-6-x } & = & -12 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -12 \color{blue}{-6} \\\Leftrightarrow &-15x & = &-18\\\Leftrightarrow & \color{red}{-15}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-18}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{-6}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-6}\color{blue}{+6-x } & = & -11 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -11 \color{blue}{+6} \\\Leftrightarrow &-8x & = &-5\\\Leftrightarrow & \color{red}{-8}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-5}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{+6}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+6}\color{blue}{-6-x } & = & 8 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 8 \color{blue}{-6} \\\Leftrightarrow &-6x & = &2\\\Leftrightarrow & \color{red}{-6}x & = &2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{+7}& = & -6 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+7}\color{blue}{-7-7x } & = & -6 \color{red}{ +7x }\color{blue}{-7-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -6 \color{blue}{-7} \\\Leftrightarrow &-17x & = &-13\\\Leftrightarrow & \color{red}{-17}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-13}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{13}{17} } & & \\ & V = \left\{ \frac{13}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{-14}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-14}\color{blue}{+14-x } & = & -7 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -7 \color{blue}{+14} \\\Leftrightarrow &-9x & = &7\\\Leftrightarrow & \color{red}{-9}x & = &7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{9} } & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)