Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{+1}& = & -8 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+1}\color{blue}{-1-13x } & = & -8 \color{red}{ +13x }\color{blue}{-1-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -8 \color{blue}{-1} \\\Leftrightarrow &-25x & = &-9\\\Leftrightarrow & \color{red}{-25}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-9}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{9}{25} } & & \\ & V = \left\{ \frac{9}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{-1}& = & 7 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{-1}\color{blue}{+1+7x } & = & 7 \color{red}{ -7x }\color{blue}{+1+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & 7 \color{blue}{+1} \\\Leftrightarrow &22x & = &8\\\Leftrightarrow & \color{red}{22}x & = &8\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{8}{22} \\\Leftrightarrow & \color{green}{ x = \frac{4}{11} } & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{-14}& = & -13 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-14}\color{blue}{+14+3x } & = & -13 \color{red}{ -3x }\color{blue}{+14+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -13 \color{blue}{+14} \\\Leftrightarrow &13x & = &1\\\Leftrightarrow & \color{red}{13}x & = &1\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{1}{13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{-6}& = & 1 \color{red}{ +13x } \\\Leftrightarrow & 15x \color{red}{-6}\color{blue}{+6-13x } & = & 1 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & 15x \color{blue}{-13x } & = & 1 \color{blue}{+6} \\\Leftrightarrow &2x & = &7\\\Leftrightarrow & \color{red}{2}x & = &7\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{7}{2} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{-14}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-14}\color{blue}{+14-x } & = & 10 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 10 \color{blue}{+14} \\\Leftrightarrow &5x & = &24\\\Leftrightarrow & \color{red}{5}x & = &24\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{24}{5} \\\Leftrightarrow & \color{green}{ x = \frac{24}{5} } & & \\ & V = \left\{ \frac{24}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{-9}& = & 1 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{-9}\color{blue}{+9-10x } & = & 1 \color{red}{ +10x }\color{blue}{+9-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & 1 \color{blue}{+9} \\\Leftrightarrow &-19x & = &10\\\Leftrightarrow & \color{red}{-19}x & = &10\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{10}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{19} } & & \\ & V = \left\{ \frac{-10}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{-15}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-15}\color{blue}{+15-x } & = & -2 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -2 \color{blue}{+15} \\\Leftrightarrow &-11x & = &13\\\Leftrightarrow & \color{red}{-11}x & = &13\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{13}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{11} } & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+6}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+6}\color{blue}{-6-x } & = & 14 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 14 \color{blue}{-6} \\\Leftrightarrow &-11x & = &8\\\Leftrightarrow & \color{red}{-11}x & = &8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{11} } & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{-3}& = & -9 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{-3}\color{blue}{+3+4x } & = & -9 \color{red}{ -4x }\color{blue}{+3+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & -9 \color{blue}{+3} \\\Leftrightarrow &9x & = &-6\\\Leftrightarrow & \color{red}{9}x & = &-6\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-6}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{-15}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-15}\color{blue}{+15-x } & = & 10 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 10 \color{blue}{+15} \\\Leftrightarrow &-9x & = &25\\\Leftrightarrow & \color{red}{-9}x & = &25\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{25}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{9} } & & \\ & V = \left\{ \frac{-25}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{-4}& = & 10 \color{red}{ +6x } \\\Leftrightarrow & 5x \color{red}{-4}\color{blue}{+4-6x } & = & 10 \color{red}{ +6x }\color{blue}{+4-6x } \\\Leftrightarrow & 5x \color{blue}{-6x } & = & 10 \color{blue}{+4} \\\Leftrightarrow &-x & = &14\\\Leftrightarrow & \color{red}{-}x & = &14\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{14}{-1} \\\Leftrightarrow & \color{green}{ x = -14 } & & \\ & V = \left\{ -14 \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{-4}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-4}\color{blue}{+4-x } & = & -7 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -7 \color{blue}{+4} \\\Leftrightarrow &-13x & = &-3\\\Leftrightarrow & \color{red}{-13}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{3}{13} } & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)