Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{+10}& = & -15 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{+10}\color{blue}{-10+10x } & = & -15 \color{red}{ -10x }\color{blue}{-10+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & -15 \color{blue}{-10} \\\Leftrightarrow &21x & = &-25\\\Leftrightarrow & \color{red}{21}x & = &-25\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-25}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{21} } & & \\ & V = \left\{ \frac{-25}{21} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{-5}& = & 15 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-5}\color{blue}{+5-9x } & = & 15 \color{red}{ +9x }\color{blue}{+5-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 15 \color{blue}{+5} \\\Leftrightarrow &-17x & = &20\\\Leftrightarrow & \color{red}{-17}x & = &20\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{20}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{17} } & & \\ & V = \left\{ \frac{-20}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{+4}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+4}\color{blue}{-4-13x } & = & -10 \color{red}{ +13x }\color{blue}{-4-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -10 \color{blue}{-4} \\\Leftrightarrow &-25x & = &-14\\\Leftrightarrow & \color{red}{-25}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-14}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{14}{25} } & & \\ & V = \left\{ \frac{14}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{-6}& = & 10 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-6}\color{blue}{+6+6x } & = & 10 \color{red}{ -6x }\color{blue}{+6+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 10 \color{blue}{+6} \\\Leftrightarrow &19x & = &16\\\Leftrightarrow & \color{red}{19}x & = &16\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{16}{19} \\\Leftrightarrow & \color{green}{ x = \frac{16}{19} } & & \\ & V = \left\{ \frac{16}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{+6}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+6}\color{blue}{-6-x } & = & -8 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -8 \color{blue}{-6} \\\Leftrightarrow &-10x & = &-14\\\Leftrightarrow & \color{red}{-10}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-14}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{-2}& = & -3 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{-2}\color{blue}{+2-10x } & = & -3 \color{red}{ +10x }\color{blue}{+2-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & -3 \color{blue}{+2} \\\Leftrightarrow &-13x & = &-1\\\Leftrightarrow & \color{red}{-13}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{-4}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-4}\color{blue}{+4-x } & = & -13 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -13 \color{blue}{+4} \\\Leftrightarrow &x & = &-9\\\Leftrightarrow & \color{red}{}x & = &-9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -9 \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{+15}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+15}\color{blue}{-15-x } & = & 12 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 12 \color{blue}{-15} \\\Leftrightarrow &-3x & = &-3\\\Leftrightarrow & \color{red}{-3}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-3}{-3} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{+7}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+7}\color{blue}{-7-x } & = & -13 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -13 \color{blue}{-7} \\\Leftrightarrow &-6x & = &-20\\\Leftrightarrow & \color{red}{-6}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-20}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{+6}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & 9x \color{red}{+6}\color{blue}{-6-13x } & = & 11 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & 9x \color{blue}{-13x } & = & 11 \color{blue}{-6} \\\Leftrightarrow &-4x & = &5\\\Leftrightarrow & \color{red}{-4}x & = &5\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{5}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{-14}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-14}\color{blue}{+14-x } & = & -7 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -7 \color{blue}{+14} \\\Leftrightarrow &-7x & = &7\\\Leftrightarrow & \color{red}{-7}x & = &7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{7}{-7} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{+3}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+3}\color{blue}{-3-x } & = & -13 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -13 \color{blue}{-3} \\\Leftrightarrow &-4x & = &-16\\\Leftrightarrow & \color{red}{-4}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-16}{-4} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)