Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{+13}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+13}\color{blue}{-13-x } & = & -7 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -7 \color{blue}{-13} \\\Leftrightarrow &-9x & = &-20\\\Leftrightarrow & \color{red}{-9}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-20}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{20}{9} } & & \\ & V = \left\{ \frac{20}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-1}& = & -14 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-1}\color{blue}{+1+11x } & = & -14 \color{red}{ -11x }\color{blue}{+1+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -14 \color{blue}{+1} \\\Leftrightarrow &23x & = &-13\\\Leftrightarrow & \color{red}{23}x & = &-13\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-13}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{23} } & & \\ & V = \left\{ \frac{-13}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{+12}& = & 11 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+12}\color{blue}{-12+3x } & = & 11 \color{red}{ -3x }\color{blue}{-12+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 11 \color{blue}{-12} \\\Leftrightarrow &13x & = &-1\\\Leftrightarrow & \color{red}{13}x & = &-1\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-1}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{-6}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-6}\color{blue}{+6-x } & = & -3 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -3 \color{blue}{+6} \\\Leftrightarrow &-13x & = &3\\\Leftrightarrow & \color{red}{-13}x & = &3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{+2}& = & 15 \color{red}{ +6x } \\\Leftrightarrow & 13x \color{red}{+2}\color{blue}{-2-6x } & = & 15 \color{red}{ +6x }\color{blue}{-2-6x } \\\Leftrightarrow & 13x \color{blue}{-6x } & = & 15 \color{blue}{-2} \\\Leftrightarrow &7x & = &13\\\Leftrightarrow & \color{red}{7}x & = &13\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{13}{7} \\\Leftrightarrow & \color{green}{ x = \frac{13}{7} } & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{-14}& = & 6 \color{red}{ -7x } \\\Leftrightarrow & -x \color{red}{-14}\color{blue}{+14+7x } & = & 6 \color{red}{ -7x }\color{blue}{+14+7x } \\\Leftrightarrow & -x \color{blue}{+7x } & = & 6 \color{blue}{+14} \\\Leftrightarrow &6x & = &20\\\Leftrightarrow & \color{red}{6}x & = &20\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{20}{6} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{-8}& = & -11 \color{red}{ +13x } \\\Leftrightarrow & 15x \color{red}{-8}\color{blue}{+8-13x } & = & -11 \color{red}{ +13x }\color{blue}{+8-13x } \\\Leftrightarrow & 15x \color{blue}{-13x } & = & -11 \color{blue}{+8} \\\Leftrightarrow &2x & = &-3\\\Leftrightarrow & \color{red}{2}x & = &-3\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-3}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{+15}& = & 8 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{+15}\color{blue}{-15+14x } & = & 8 \color{red}{ -14x }\color{blue}{-15+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & 8 \color{blue}{-15} \\\Leftrightarrow &19x & = &-7\\\Leftrightarrow & \color{red}{19}x & = &-7\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-7}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{19} } & & \\ & V = \left\{ \frac{-7}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{-6}& = & 4 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{-6}\color{blue}{+6+5x } & = & 4 \color{red}{ -5x }\color{blue}{+6+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & 4 \color{blue}{+6} \\\Leftrightarrow &16x & = &10\\\Leftrightarrow & \color{red}{16}x & = &10\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{10}{16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{+3}& = & 6 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+3}\color{blue}{-3-13x } & = & 6 \color{red}{ +13x }\color{blue}{-3-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 6 \color{blue}{-3} \\\Leftrightarrow &-25x & = &3\\\Leftrightarrow & \color{red}{-25}x & = &3\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{3}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{25} } & & \\ & V = \left\{ \frac{-3}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{+2}& = & -9 \color{red}{ +5x } \\\Leftrightarrow & 4x \color{red}{+2}\color{blue}{-2-5x } & = & -9 \color{red}{ +5x }\color{blue}{-2-5x } \\\Leftrightarrow & 4x \color{blue}{-5x } & = & -9 \color{blue}{-2} \\\Leftrightarrow &-x & = &-11\\\Leftrightarrow & \color{red}{-}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-11}{-1} \\\Leftrightarrow & \color{green}{ x = 11 } & & \\ & V = \left\{ 11 \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{-10}& = & -8 \color{red}{ +3x } \\\Leftrightarrow & 4x \color{red}{-10}\color{blue}{+10-3x } & = & -8 \color{red}{ +3x }\color{blue}{+10-3x } \\\Leftrightarrow & 4x \color{blue}{-3x } & = & -8 \color{blue}{+10} \\\Leftrightarrow &x & = &2\\\Leftrightarrow & \color{red}{}x & = &2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 2 \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)