Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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