Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{-2}& = & 3 \color{red}{ +9x } \\\Leftrightarrow & 5x \color{red}{-2}\color{blue}{+2-9x } & = & 3 \color{red}{ +9x }\color{blue}{+2-9x } \\\Leftrightarrow & 5x \color{blue}{-9x } & = & 3 \color{blue}{+2} \\\Leftrightarrow &-4x & = &5\\\Leftrightarrow & \color{red}{-4}x & = &5\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{5}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-12}& = & -12 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{-12}\color{blue}{+12-7x } & = & -12 \color{red}{ +7x }\color{blue}{+12-7x } \\\Leftrightarrow & 12x \color{blue}{-7x } & = & -12 \color{blue}{+12} \\\Leftrightarrow &5x & = &0\\\Leftrightarrow & \color{red}{5}x & = &0\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{0}{5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{-11}& = & 15 \color{red}{ -13x } \\\Leftrightarrow & x \color{red}{-11}\color{blue}{+11+13x } & = & 15 \color{red}{ -13x }\color{blue}{+11+13x } \\\Leftrightarrow & x \color{blue}{+13x } & = & 15 \color{blue}{+11} \\\Leftrightarrow &14x & = &26\\\Leftrightarrow & \color{red}{14}x & = &26\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{26}{14} \\\Leftrightarrow & \color{green}{ x = \frac{13}{7} } & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{-2}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-2}\color{blue}{+2-x } & = & -1 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -1 \color{blue}{+2} \\\Leftrightarrow &-7x & = &1\\\Leftrightarrow & \color{red}{-7}x & = &1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{+6}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+6}\color{blue}{-6-x } & = & 1 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 1 \color{blue}{-6} \\\Leftrightarrow &7x & = &-5\\\Leftrightarrow & \color{red}{7}x & = &-5\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-5}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{+8}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+8}\color{blue}{-8-x } & = & -10 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -10 \color{blue}{-8} \\\Leftrightarrow &-7x & = &-18\\\Leftrightarrow & \color{red}{-7}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-18}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{18}{7} } & & \\ & V = \left\{ \frac{18}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{+8}& = & 11 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{+8}\color{blue}{-8+10x } & = & 11 \color{red}{ -10x }\color{blue}{-8+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & 11 \color{blue}{-8} \\\Leftrightarrow &17x & = &3\\\Leftrightarrow & \color{red}{17}x & = &3\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{3}{17} \\\Leftrightarrow & \color{green}{ x = \frac{3}{17} } & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{-9}& = & 13 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-9}\color{blue}{+9+11x } & = & 13 \color{red}{ -11x }\color{blue}{+9+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 13 \color{blue}{+9} \\\Leftrightarrow &23x & = &22\\\Leftrightarrow & \color{red}{23}x & = &22\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{22}{23} \\\Leftrightarrow & \color{green}{ x = \frac{22}{23} } & & \\ & V = \left\{ \frac{22}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{+12}& = & -7 \color{red}{ +14x } \\\Leftrightarrow & 9x \color{red}{+12}\color{blue}{-12-14x } & = & -7 \color{red}{ +14x }\color{blue}{-12-14x } \\\Leftrightarrow & 9x \color{blue}{-14x } & = & -7 \color{blue}{-12} \\\Leftrightarrow &-5x & = &-19\\\Leftrightarrow & \color{red}{-5}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-19}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{19}{5} } & & \\ & V = \left\{ \frac{19}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{-12}& = & 11 \color{red}{ +8x } \\\Leftrightarrow & 7x \color{red}{-12}\color{blue}{+12-8x } & = & 11 \color{red}{ +8x }\color{blue}{+12-8x } \\\Leftrightarrow & 7x \color{blue}{-8x } & = & 11 \color{blue}{+12} \\\Leftrightarrow &-x & = &23\\\Leftrightarrow & \color{red}{-}x & = &23\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{23}{-1} \\\Leftrightarrow & \color{green}{ x = -23 } & & \\ & V = \left\{ -23 \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{+14}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+14}\color{blue}{-14-x } & = & -12 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -12 \color{blue}{-14} \\\Leftrightarrow &-8x & = &-26\\\Leftrightarrow & \color{red}{-8}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-26}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{13}{4} } & & \\ & V = \left\{ \frac{13}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{+11}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+11}\color{blue}{-11-13x } & = & -10 \color{red}{ +13x }\color{blue}{-11-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -10 \color{blue}{-11} \\\Leftrightarrow &-19x & = &-21\\\Leftrightarrow & \color{red}{-19}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-21}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{21}{19} } & & \\ & V = \left\{ \frac{21}{19} \right\} & \\\end{align}\)