Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{-2}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-2}\color{blue}{+2-x } & = & -13 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -13 \color{blue}{+2} \\\Leftrightarrow &-12x & = &-11\\\Leftrightarrow & \color{red}{-12}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-11}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{11}{12} } & & \\ & V = \left\{ \frac{11}{12} \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{-4}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-4}\color{blue}{+4-x } & = & -6 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -6 \color{blue}{+4} \\\Leftrightarrow &-13x & = &-2\\\Leftrightarrow & \color{red}{-13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{-12}& = & 9 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{-12}\color{blue}{+12-5x } & = & 9 \color{red}{ +5x }\color{blue}{+12-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & 9 \color{blue}{+12} \\\Leftrightarrow &-9x & = &21\\\Leftrightarrow & \color{red}{-9}x & = &21\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{21}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{-6}& = & -2 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-6}\color{blue}{+6-13x } & = & -2 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -2 \color{blue}{+6} \\\Leftrightarrow &-19x & = &4\\\Leftrightarrow & \color{red}{-19}x & = &4\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{4}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{19} } & & \\ & V = \left\{ \frac{-4}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{+5}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+5}\color{blue}{-5-x } & = & 7 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 7 \color{blue}{-5} \\\Leftrightarrow &x & = &2\\\Leftrightarrow & \color{red}{}x & = &2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 2 \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{+8}& = & -10 \color{red}{ -7x } \\\Leftrightarrow & 5x \color{red}{+8}\color{blue}{-8+7x } & = & -10 \color{red}{ -7x }\color{blue}{-8+7x } \\\Leftrightarrow & 5x \color{blue}{+7x } & = & -10 \color{blue}{-8} \\\Leftrightarrow &12x & = &-18\\\Leftrightarrow & \color{red}{12}x & = &-18\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-18}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{+4}& = & 10 \color{red}{ +13x } \\\Leftrightarrow & 2x \color{red}{+4}\color{blue}{-4-13x } & = & 10 \color{red}{ +13x }\color{blue}{-4-13x } \\\Leftrightarrow & 2x \color{blue}{-13x } & = & 10 \color{blue}{-4} \\\Leftrightarrow &-11x & = &6\\\Leftrightarrow & \color{red}{-11}x & = &6\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{6}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{-12}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-12}\color{blue}{+12-x } & = & -8 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -8 \color{blue}{+12} \\\Leftrightarrow &-14x & = &4\\\Leftrightarrow & \color{red}{-14}x & = &4\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{4}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{+4}& = & -5 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+4}\color{blue}{-4-9x } & = & -5 \color{red}{ +9x }\color{blue}{-4-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -5 \color{blue}{-4} \\\Leftrightarrow &-17x & = &-9\\\Leftrightarrow & \color{red}{-17}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-9}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{9}{17} } & & \\ & V = \left\{ \frac{9}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{+6}& = & -4 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{+6}\color{blue}{-6-3x } & = & -4 \color{red}{ +3x }\color{blue}{-6-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & -4 \color{blue}{-6} \\\Leftrightarrow &-x & = &-10\\\Leftrightarrow & \color{red}{-}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-10}{-1} \\\Leftrightarrow & \color{green}{ x = 10 } & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{-10}& = & -13 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{-10}\color{blue}{+10+14x } & = & -13 \color{red}{ -14x }\color{blue}{+10+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & -13 \color{blue}{+10} \\\Leftrightarrow &19x & = &-3\\\Leftrightarrow & \color{red}{19}x & = &-3\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-3}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{19} } & & \\ & V = \left\{ \frac{-3}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{-6}& = & 12 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{-6}\color{blue}{+6+4x } & = & 12 \color{red}{ -4x }\color{blue}{+6+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & 12 \color{blue}{+6} \\\Leftrightarrow &9x & = &18\\\Leftrightarrow & \color{red}{9}x & = &18\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{18}{9} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)