Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{+3}& = & 1 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{+3}\color{blue}{-3+4x } & = & 1 \color{red}{ -4x }\color{blue}{-3+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & 1 \color{blue}{-3} \\\Leftrightarrow &9x & = &-2\\\Leftrightarrow & \color{red}{9}x & = &-2\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-2}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{+11}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+11}\color{blue}{-11-x } & = & -8 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -8 \color{blue}{-11} \\\Leftrightarrow &-4x & = &-19\\\Leftrightarrow & \color{red}{-4}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-19}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{19}{4} } & & \\ & V = \left\{ \frac{19}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{-15}& = & -5 \color{red}{ +14x } \\\Leftrightarrow & 13x \color{red}{-15}\color{blue}{+15-14x } & = & -5 \color{red}{ +14x }\color{blue}{+15-14x } \\\Leftrightarrow & 13x \color{blue}{-14x } & = & -5 \color{blue}{+15} \\\Leftrightarrow &-x & = &10\\\Leftrightarrow & \color{red}{-}x & = &10\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{10}{-1} \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{+8}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+8}\color{blue}{-8-x } & = & 14 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 14 \color{blue}{-8} \\\Leftrightarrow &-14x & = &6\\\Leftrightarrow & \color{red}{-14}x & = &6\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{6}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{-12}& = & 4 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{-12}\color{blue}{+12+7x } & = & 4 \color{red}{ -7x }\color{blue}{+12+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & 4 \color{blue}{+12} \\\Leftrightarrow &11x & = &16\\\Leftrightarrow & \color{red}{11}x & = &16\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{16}{11} \\\Leftrightarrow & \color{green}{ x = \frac{16}{11} } & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{-14}& = & 6 \color{red}{ +11x } \\\Leftrightarrow & 13x \color{red}{-14}\color{blue}{+14-11x } & = & 6 \color{red}{ +11x }\color{blue}{+14-11x } \\\Leftrightarrow & 13x \color{blue}{-11x } & = & 6 \color{blue}{+14} \\\Leftrightarrow &2x & = &20\\\Leftrightarrow & \color{red}{2}x & = &20\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{20}{2} \\\Leftrightarrow & \color{green}{ x = 10 } & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{+10}& = & -8 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+10}\color{blue}{-10+13x } & = & -8 \color{red}{ -13x }\color{blue}{-10+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -8 \color{blue}{-10} \\\Leftrightarrow &23x & = &-18\\\Leftrightarrow & \color{red}{23}x & = &-18\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-18}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{23} } & & \\ & V = \left\{ \frac{-18}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{-2}& = & 8 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{-2}\color{blue}{+2-13x } & = & 8 \color{red}{ +13x }\color{blue}{+2-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & 8 \color{blue}{+2} \\\Leftrightarrow &-17x & = &10\\\Leftrightarrow & \color{red}{-17}x & = &10\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{10}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{17} } & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{-13}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{-13}\color{blue}{+13-7x } & = & 11 \color{red}{ +7x }\color{blue}{+13-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & 11 \color{blue}{+13} \\\Leftrightarrow &-5x & = &24\\\Leftrightarrow & \color{red}{-5}x & = &24\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{24}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{5} } & & \\ & V = \left\{ \frac{-24}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{-3}& = & 5 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-3}\color{blue}{+3-9x } & = & 5 \color{red}{ +9x }\color{blue}{+3-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & 5 \color{blue}{+3} \\\Leftrightarrow &-13x & = &8\\\Leftrightarrow & \color{red}{-13}x & = &8\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{8}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{13} } & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{-8}& = & -4 \color{red}{ +4x } \\\Leftrightarrow & 7x \color{red}{-8}\color{blue}{+8-4x } & = & -4 \color{red}{ +4x }\color{blue}{+8-4x } \\\Leftrightarrow & 7x \color{blue}{-4x } & = & -4 \color{blue}{+8} \\\Leftrightarrow &3x & = &4\\\Leftrightarrow & \color{red}{3}x & = &4\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{4}{3} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{+10}& = & -5 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+10}\color{blue}{-10-9x } & = & -5 \color{red}{ +9x }\color{blue}{-10-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -5 \color{blue}{-10} \\\Leftrightarrow &-17x & = &-15\\\Leftrightarrow & \color{red}{-17}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-15}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{15}{17} } & & \\ & V = \left\{ \frac{15}{17} \right\} & \\\end{align}\)