Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{+11}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+11}\color{blue}{-11-x } & = & -3 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -3 \color{blue}{-11} \\\Leftrightarrow &-9x & = &-14\\\Leftrightarrow & \color{red}{-9}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-14}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{14}{9} } & & \\ & V = \left\{ \frac{14}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{+4}& = & -14 \color{red}{ +2x } \\\Leftrightarrow & 5x \color{red}{+4}\color{blue}{-4-2x } & = & -14 \color{red}{ +2x }\color{blue}{-4-2x } \\\Leftrightarrow & 5x \color{blue}{-2x } & = & -14 \color{blue}{-4} \\\Leftrightarrow &3x & = &-18\\\Leftrightarrow & \color{red}{3}x & = &-18\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-18}{3} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{+1}& = & 12 \color{red}{ -13x } \\\Leftrightarrow & -x \color{red}{+1}\color{blue}{-1+13x } & = & 12 \color{red}{ -13x }\color{blue}{-1+13x } \\\Leftrightarrow & -x \color{blue}{+13x } & = & 12 \color{blue}{-1} \\\Leftrightarrow &12x & = &11\\\Leftrightarrow & \color{red}{12}x & = &11\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{11}{12} \\\Leftrightarrow & \color{green}{ x = \frac{11}{12} } & & \\ & V = \left\{ \frac{11}{12} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{-9}& = & -6 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{-9}\color{blue}{+9+11x } & = & -6 \color{red}{ -11x }\color{blue}{+9+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & -6 \color{blue}{+9} \\\Leftrightarrow &26x & = &3\\\Leftrightarrow & \color{red}{26}x & = &3\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{3}{26} \\\Leftrightarrow & \color{green}{ x = \frac{3}{26} } & & \\ & V = \left\{ \frac{3}{26} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+6}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+6}\color{blue}{-6-x } & = & -3 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -3 \color{blue}{-6} \\\Leftrightarrow &-9x & = &-9\\\Leftrightarrow & \color{red}{-9}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-9}{-9} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{+2}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+2}\color{blue}{-2-x } & = & 11 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 11 \color{blue}{-2} \\\Leftrightarrow &-4x & = &9\\\Leftrightarrow & \color{red}{-4}x & = &9\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{9}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{4} } & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{-11}& = & -14 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{-11}\color{blue}{+11+12x } & = & -14 \color{red}{ -12x }\color{blue}{+11+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & -14 \color{blue}{+11} \\\Leftrightarrow &25x & = &-3\\\Leftrightarrow & \color{red}{25}x & = &-3\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-3}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{25} } & & \\ & V = \left\{ \frac{-3}{25} \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{+7}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+7}\color{blue}{-7-x } & = & -14 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -14 \color{blue}{-7} \\\Leftrightarrow &-7x & = &-21\\\Leftrightarrow & \color{red}{-7}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-21}{-7} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{-5}& = & 3 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{-5}\color{blue}{+5+12x } & = & 3 \color{red}{ -12x }\color{blue}{+5+12x } \\\Leftrightarrow & 5x \color{blue}{+12x } & = & 3 \color{blue}{+5} \\\Leftrightarrow &17x & = &8\\\Leftrightarrow & \color{red}{17}x & = &8\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{8}{17} \\\Leftrightarrow & \color{green}{ x = \frac{8}{17} } & & \\ & V = \left\{ \frac{8}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{-4}& = & 12 \color{red}{ +4x } \\\Leftrightarrow & 9x \color{red}{-4}\color{blue}{+4-4x } & = & 12 \color{red}{ +4x }\color{blue}{+4-4x } \\\Leftrightarrow & 9x \color{blue}{-4x } & = & 12 \color{blue}{+4} \\\Leftrightarrow &5x & = &16\\\Leftrightarrow & \color{red}{5}x & = &16\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{16}{5} \\\Leftrightarrow & \color{green}{ x = \frac{16}{5} } & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{+6}& = & -5 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{+6}\color{blue}{-6-13x } & = & -5 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & -5 \color{blue}{-6} \\\Leftrightarrow &-17x & = &-11\\\Leftrightarrow & \color{red}{-17}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-11}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{11}{17} } & & \\ & V = \left\{ \frac{11}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{-15}& = & -10 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{-15}\color{blue}{+15-12x } & = & -10 \color{red}{ +12x }\color{blue}{+15-12x } \\\Leftrightarrow & 11x \color{blue}{-12x } & = & -10 \color{blue}{+15} \\\Leftrightarrow &-x & = &5\\\Leftrightarrow & \color{red}{-}x & = &5\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{5}{-1} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)