Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{+2}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+2}\color{blue}{-2-x } & = & -11 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -11 \color{blue}{-2} \\\Leftrightarrow &-3x & = &-13\\\Leftrightarrow & \color{red}{-3}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-13}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{13}{3} } & & \\ & V = \left\{ \frac{13}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{-4}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-4}\color{blue}{+4-x } & = & 5 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 5 \color{blue}{+4} \\\Leftrightarrow &-11x & = &9\\\Leftrightarrow & \color{red}{-11}x & = &9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{11} } & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{+1}& = & -4 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+1}\color{blue}{-1+2x } & = & -4 \color{red}{ -2x }\color{blue}{-1+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -4 \color{blue}{-1} \\\Leftrightarrow &17x & = &-5\\\Leftrightarrow & \color{red}{17}x & = &-5\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-5}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{17} } & & \\ & V = \left\{ \frac{-5}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{+6}& = & -5 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+6}\color{blue}{-6-x } & = & -5 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -5 \color{blue}{-6} \\\Leftrightarrow &x & = &-11\\\Leftrightarrow & \color{red}{}x & = &-11\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -11 \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{-3}& = & -13 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{-3}\color{blue}{+3-13x } & = & -13 \color{red}{ +13x }\color{blue}{+3-13x } \\\Leftrightarrow & 12x \color{blue}{-13x } & = & -13 \color{blue}{+3} \\\Leftrightarrow &-x & = &-10\\\Leftrightarrow & \color{red}{-}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-10}{-1} \\\Leftrightarrow & \color{green}{ x = 10 } & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{+8}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+8}\color{blue}{-8-x } & = & 5 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 5 \color{blue}{-8} \\\Leftrightarrow &-15x & = &-3\\\Leftrightarrow & \color{red}{-15}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{+2}& = & 3 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{+2}\color{blue}{-2-9x } & = & 3 \color{red}{ +9x }\color{blue}{-2-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & 3 \color{blue}{-2} \\\Leftrightarrow &5x & = &1\\\Leftrightarrow & \color{red}{5}x & = &1\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{1}{5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{+10}& = & -8 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+10}\color{blue}{-10+13x } & = & -8 \color{red}{ -13x }\color{blue}{-10+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -8 \color{blue}{-10} \\\Leftrightarrow &27x & = &-18\\\Leftrightarrow & \color{red}{27}x & = &-18\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-18}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{-9}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-9}\color{blue}{+9-x } & = & 11 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 11 \color{blue}{+9} \\\Leftrightarrow &-3x & = &20\\\Leftrightarrow & \color{red}{-3}x & = &20\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{20}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{3} } & & \\ & V = \left\{ \frac{-20}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{-12}& = & -2 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{-12}\color{blue}{+12-7x } & = & -2 \color{red}{ +7x }\color{blue}{+12-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & -2 \color{blue}{+12} \\\Leftrightarrow &-5x & = &10\\\Leftrightarrow & \color{red}{-5}x & = &10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{10}{-5} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{+3}& = & -13 \color{red}{ -8x } \\\Leftrightarrow & 11x \color{red}{+3}\color{blue}{-3+8x } & = & -13 \color{red}{ -8x }\color{blue}{-3+8x } \\\Leftrightarrow & 11x \color{blue}{+8x } & = & -13 \color{blue}{-3} \\\Leftrightarrow &19x & = &-16\\\Leftrightarrow & \color{red}{19}x & = &-16\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-16}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{19} } & & \\ & V = \left\{ \frac{-16}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{-10}& = & 10 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-10}\color{blue}{+10-14x } & = & 10 \color{red}{ +14x }\color{blue}{+10-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & 10 \color{blue}{+10} \\\Leftrightarrow &-27x & = &20\\\Leftrightarrow & \color{red}{-27}x & = &20\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{20}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{27} } & & \\ & V = \left\{ \frac{-20}{27} \right\} & \\\end{align}\)