Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{-10}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-10}\color{blue}{+10-x } & = & 11 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 11 \color{blue}{+10} \\\Leftrightarrow &-11x & = &21\\\Leftrightarrow & \color{red}{-11}x & = &21\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{21}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{11} } & & \\ & V = \left\{ \frac{-21}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{-13}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-13}\color{blue}{+13-x } & = & 10 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 10 \color{blue}{+13} \\\Leftrightarrow &7x & = &23\\\Leftrightarrow & \color{red}{7}x & = &23\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{23}{7} \\\Leftrightarrow & \color{green}{ x = \frac{23}{7} } & & \\ & V = \left\{ \frac{23}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{-3}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-3}\color{blue}{+3-x } & = & 13 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 13 \color{blue}{+3} \\\Leftrightarrow &-12x & = &16\\\Leftrightarrow & \color{red}{-12}x & = &16\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{16}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{+7}& = & -6 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{+7}\color{blue}{-7-4x } & = & -6 \color{red}{ +4x }\color{blue}{-7-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & -6 \color{blue}{-7} \\\Leftrightarrow &-7x & = &-13\\\Leftrightarrow & \color{red}{-7}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-13}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{13}{7} } & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{+12}& = & -15 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{+12}\color{blue}{-12-3x } & = & -15 \color{red}{ +3x }\color{blue}{-12-3x } \\\Leftrightarrow & -2x \color{blue}{-3x } & = & -15 \color{blue}{-12} \\\Leftrightarrow &-5x & = &-27\\\Leftrightarrow & \color{red}{-5}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-27}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{27}{5} } & & \\ & V = \left\{ \frac{27}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{-6}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-6}\color{blue}{+6-x } & = & -8 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -8 \color{blue}{+6} \\\Leftrightarrow &-6x & = &-2\\\Leftrightarrow & \color{red}{-6}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{+11}& = & 13 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{+11}\color{blue}{-11+15x } & = & 13 \color{red}{ -15x }\color{blue}{-11+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & 13 \color{blue}{-11} \\\Leftrightarrow &19x & = &2\\\Leftrightarrow & \color{red}{19}x & = &2\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{2}{19} \\\Leftrightarrow & \color{green}{ x = \frac{2}{19} } & & \\ & V = \left\{ \frac{2}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{-14}& = & -11 \color{red}{ +12x } \\\Leftrightarrow & x \color{red}{-14}\color{blue}{+14-12x } & = & -11 \color{red}{ +12x }\color{blue}{+14-12x } \\\Leftrightarrow & x \color{blue}{-12x } & = & -11 \color{blue}{+14} \\\Leftrightarrow &-11x & = &3\\\Leftrightarrow & \color{red}{-11}x & = &3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{+6}& = & -3 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{+6}\color{blue}{-6+4x } & = & -3 \color{red}{ -4x }\color{blue}{-6+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -3 \color{blue}{-6} \\\Leftrightarrow &13x & = &-9\\\Leftrightarrow & \color{red}{13}x & = &-9\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-9}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{13} } & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{+5}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{+5}\color{blue}{-5-13x } & = & -10 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & -10 \color{blue}{-5} \\\Leftrightarrow &-3x & = &-15\\\Leftrightarrow & \color{red}{-3}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-15}{-3} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{-5}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-5}\color{blue}{+5-x } & = & 10 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 10 \color{blue}{+5} \\\Leftrightarrow &-6x & = &15\\\Leftrightarrow & \color{red}{-6}x & = &15\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{15}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{-6}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-6}\color{blue}{+6-13x } & = & 3 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 3 \color{blue}{+6} \\\Leftrightarrow &-25x & = &9\\\Leftrightarrow & \color{red}{-25}x & = &9\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{9}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{25} } & & \\ & V = \left\{ \frac{-9}{25} \right\} & \\\end{align}\)