Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{+8}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{+8}\color{blue}{-8-11x } & = & -3 \color{red}{ +11x }\color{blue}{-8-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & -3 \color{blue}{-8} \\\Leftrightarrow &x & = &-11\\\Leftrightarrow & \color{red}{}x & = &-11\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -11 \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{+4}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+4}\color{blue}{-4-x } & = & 10 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 10 \color{blue}{-4} \\\Leftrightarrow &-5x & = &6\\\Leftrightarrow & \color{red}{-5}x & = &6\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{6}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{+2}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+2}\color{blue}{-2-x } & = & 5 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 5 \color{blue}{-2} \\\Leftrightarrow &-4x & = &3\\\Leftrightarrow & \color{red}{-4}x & = &3\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{3}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{-8}& = & 12 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{-8}\color{blue}{+8-14x } & = & 12 \color{red}{ +14x }\color{blue}{+8-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & 12 \color{blue}{+8} \\\Leftrightarrow &-25x & = &20\\\Leftrightarrow & \color{red}{-25}x & = &20\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{20}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+12}& = & 13 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+12}\color{blue}{-12-9x } & = & 13 \color{red}{ +9x }\color{blue}{-12-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 13 \color{blue}{-12} \\\Leftrightarrow &-17x & = &1\\\Leftrightarrow & \color{red}{-17}x & = &1\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{1}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{17} } & & \\ & V = \left\{ \frac{-1}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{-5}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-5}\color{blue}{+5-x } & = & -9 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -9 \color{blue}{+5} \\\Leftrightarrow &-11x & = &-4\\\Leftrightarrow & \color{red}{-11}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-4}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{4}{11} } & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{+3}& = & -8 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{+3}\color{blue}{-3-4x } & = & -8 \color{red}{ +4x }\color{blue}{-3-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & -8 \color{blue}{-3} \\\Leftrightarrow &-19x & = &-11\\\Leftrightarrow & \color{red}{-19}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-11}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{11}{19} } & & \\ & V = \left\{ \frac{11}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{-9}& = & 15 \color{red}{ +3x } \\\Leftrightarrow & 8x \color{red}{-9}\color{blue}{+9-3x } & = & 15 \color{red}{ +3x }\color{blue}{+9-3x } \\\Leftrightarrow & 8x \color{blue}{-3x } & = & 15 \color{blue}{+9} \\\Leftrightarrow &5x & = &24\\\Leftrightarrow & \color{red}{5}x & = &24\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{24}{5} \\\Leftrightarrow & \color{green}{ x = \frac{24}{5} } & & \\ & V = \left\{ \frac{24}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{-10}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-10}\color{blue}{+10-x } & = & 15 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 15 \color{blue}{+10} \\\Leftrightarrow &-9x & = &25\\\Leftrightarrow & \color{red}{-9}x & = &25\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{25}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{9} } & & \\ & V = \left\{ \frac{-25}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & 15x \color{red}{+4}& = & -5 \color{red}{ +2x } \\\Leftrightarrow & 15x \color{red}{+4}\color{blue}{-4-2x } & = & -5 \color{red}{ +2x }\color{blue}{-4-2x } \\\Leftrightarrow & 15x \color{blue}{-2x } & = & -5 \color{blue}{-4} \\\Leftrightarrow &13x & = &-9\\\Leftrightarrow & \color{red}{13}x & = &-9\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-9}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{13} } & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{-2}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-2}\color{blue}{+2-x } & = & -9 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -9 \color{blue}{+2} \\\Leftrightarrow &-5x & = &-7\\\Leftrightarrow & \color{red}{-5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{+3}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{+3}\color{blue}{-3-x } & = & 13 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & 13 \color{blue}{-3} \\\Leftrightarrow &3x & = &10\\\Leftrightarrow & \color{red}{3}x & = &10\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{10}{3} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)