Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{-14}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-14}\color{blue}{+14-x } & = & -8 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -8 \color{blue}{+14} \\\Leftrightarrow &13x & = &6\\\Leftrightarrow & \color{red}{13}x & = &6\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{6}{13} \\\Leftrightarrow & \color{green}{ x = \frac{6}{13} } & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{-3}& = & 10 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-3}\color{blue}{+3+13x } & = & 10 \color{red}{ -13x }\color{blue}{+3+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 10 \color{blue}{+3} \\\Leftrightarrow &27x & = &13\\\Leftrightarrow & \color{red}{27}x & = &13\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{13}{27} \\\Leftrightarrow & \color{green}{ x = \frac{13}{27} } & & \\ & V = \left\{ \frac{13}{27} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{+8}& = & -7 \color{red}{ +4x } \\\Leftrightarrow & 9x \color{red}{+8}\color{blue}{-8-4x } & = & -7 \color{red}{ +4x }\color{blue}{-8-4x } \\\Leftrightarrow & 9x \color{blue}{-4x } & = & -7 \color{blue}{-8} \\\Leftrightarrow &5x & = &-15\\\Leftrightarrow & \color{red}{5}x & = &-15\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-15}{5} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{-9}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-9}\color{blue}{+9-x } & = & -2 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -2 \color{blue}{+9} \\\Leftrightarrow &-14x & = &7\\\Leftrightarrow & \color{red}{-14}x & = &7\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{7}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{-5}& = & -5 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-5}\color{blue}{+5-7x } & = & -5 \color{red}{ +7x }\color{blue}{+5-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -5 \color{blue}{+5} \\\Leftrightarrow &-13x & = &0\\\Leftrightarrow & \color{red}{-13}x & = &0\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{0}{-13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{+3}& = & -11 \color{red}{ -11x } \\\Leftrightarrow & -x \color{red}{+3}\color{blue}{-3+11x } & = & -11 \color{red}{ -11x }\color{blue}{-3+11x } \\\Leftrightarrow & -x \color{blue}{+11x } & = & -11 \color{blue}{-3} \\\Leftrightarrow &10x & = &-14\\\Leftrightarrow & \color{red}{10}x & = &-14\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-14}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{+11}& = & 10 \color{red}{ +13x } \\\Leftrightarrow & 7x \color{red}{+11}\color{blue}{-11-13x } & = & 10 \color{red}{ +13x }\color{blue}{-11-13x } \\\Leftrightarrow & 7x \color{blue}{-13x } & = & 10 \color{blue}{-11} \\\Leftrightarrow &-6x & = &-1\\\Leftrightarrow & \color{red}{-6}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-1}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{-13}& = & 11 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{-13}\color{blue}{+13-5x } & = & 11 \color{red}{ +5x }\color{blue}{+13-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & 11 \color{blue}{+13} \\\Leftrightarrow &-17x & = &24\\\Leftrightarrow & \color{red}{-17}x & = &24\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{24}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{17} } & & \\ & V = \left\{ \frac{-24}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{+10}& = & 14 \color{red}{ +3x } \\\Leftrightarrow & -14x \color{red}{+10}\color{blue}{-10-3x } & = & 14 \color{red}{ +3x }\color{blue}{-10-3x } \\\Leftrightarrow & -14x \color{blue}{-3x } & = & 14 \color{blue}{-10} \\\Leftrightarrow &-17x & = &4\\\Leftrightarrow & \color{red}{-17}x & = &4\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{4}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{17} } & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{+3}& = & 6 \color{red}{ +14x } \\\Leftrightarrow & 3x \color{red}{+3}\color{blue}{-3-14x } & = & 6 \color{red}{ +14x }\color{blue}{-3-14x } \\\Leftrightarrow & 3x \color{blue}{-14x } & = & 6 \color{blue}{-3} \\\Leftrightarrow &-11x & = &3\\\Leftrightarrow & \color{red}{-11}x & = &3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{-2}& = & -8 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{-2}\color{blue}{+2-7x } & = & -8 \color{red}{ +7x }\color{blue}{+2-7x } \\\Leftrightarrow & 12x \color{blue}{-7x } & = & -8 \color{blue}{+2} \\\Leftrightarrow &5x & = &-6\\\Leftrightarrow & \color{red}{5}x & = &-6\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-6}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{+15}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+15}\color{blue}{-15-x } & = & -14 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -14 \color{blue}{-15} \\\Leftrightarrow &-14x & = &-29\\\Leftrightarrow & \color{red}{-14}x & = &-29\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-29}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{29}{14} } & & \\ & V = \left\{ \frac{29}{14} \right\} & \\\end{align}\)