Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{-14}& = & 2 \color{red}{ -12x } \\\Leftrightarrow & -x \color{red}{-14}\color{blue}{+14+12x } & = & 2 \color{red}{ -12x }\color{blue}{+14+12x } \\\Leftrightarrow & -x \color{blue}{+12x } & = & 2 \color{blue}{+14} \\\Leftrightarrow &11x & = &16\\\Leftrightarrow & \color{red}{11}x & = &16\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{16}{11} \\\Leftrightarrow & \color{green}{ x = \frac{16}{11} } & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{-2}& = & 11 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{-2}\color{blue}{+2-3x } & = & 11 \color{red}{ +3x }\color{blue}{+2-3x } \\\Leftrightarrow & -2x \color{blue}{-3x } & = & 11 \color{blue}{+2} \\\Leftrightarrow &-5x & = &13\\\Leftrightarrow & \color{red}{-5}x & = &13\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{13}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{5} } & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{+6}& = & -11 \color{red}{ +13x } \\\Leftrightarrow & 9x \color{red}{+6}\color{blue}{-6-13x } & = & -11 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & 9x \color{blue}{-13x } & = & -11 \color{blue}{-6} \\\Leftrightarrow &-4x & = &-17\\\Leftrightarrow & \color{red}{-4}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-17}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{17}{4} } & & \\ & V = \left\{ \frac{17}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{-11}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-11}\color{blue}{+11-x } & = & 3 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 3 \color{blue}{+11} \\\Leftrightarrow &-12x & = &14\\\Leftrightarrow & \color{red}{-12}x & = &14\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{14}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{6} } & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{-6}& = & 6 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-6}\color{blue}{+6-7x } & = & 6 \color{red}{ +7x }\color{blue}{+6-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 6 \color{blue}{+6} \\\Leftrightarrow &3x & = &12\\\Leftrightarrow & \color{red}{3}x & = &12\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{12}{3} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{-11}& = & 9 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{-11}\color{blue}{+11+2x } & = & 9 \color{red}{ -2x }\color{blue}{+11+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & 9 \color{blue}{+11} \\\Leftrightarrow &13x & = &20\\\Leftrightarrow & \color{red}{13}x & = &20\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{20}{13} \\\Leftrightarrow & \color{green}{ x = \frac{20}{13} } & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{-12}& = & 13 \color{red}{ +5x } \\\Leftrightarrow & 11x \color{red}{-12}\color{blue}{+12-5x } & = & 13 \color{red}{ +5x }\color{blue}{+12-5x } \\\Leftrightarrow & 11x \color{blue}{-5x } & = & 13 \color{blue}{+12} \\\Leftrightarrow &6x & = &25\\\Leftrightarrow & \color{red}{6}x & = &25\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{25}{6} \\\Leftrightarrow & \color{green}{ x = \frac{25}{6} } & & \\ & V = \left\{ \frac{25}{6} \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{-11}& = & 13 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{-11}\color{blue}{+11-4x } & = & 13 \color{red}{ +4x }\color{blue}{+11-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & 13 \color{blue}{+11} \\\Leftrightarrow &-7x & = &24\\\Leftrightarrow & \color{red}{-7}x & = &24\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{24}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{7} } & & \\ & V = \left\{ \frac{-24}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{+13}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{+13}\color{blue}{-13-x } & = & 7 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & 7 \color{blue}{-13} \\\Leftrightarrow &4x & = &-6\\\Leftrightarrow & \color{red}{4}x & = &-6\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-6}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{+15}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+15}\color{blue}{-15-x } & = & 5 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 5 \color{blue}{-15} \\\Leftrightarrow &-14x & = &-10\\\Leftrightarrow & \color{red}{-14}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-10}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{+5}& = & 6 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{+5}\color{blue}{-5+15x } & = & 6 \color{red}{ -15x }\color{blue}{-5+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & 6 \color{blue}{-5} \\\Leftrightarrow &19x & = &1\\\Leftrightarrow & \color{red}{19}x & = &1\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{1}{19} \\\Leftrightarrow & \color{green}{ x = \frac{1}{19} } & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{-15}& = & 6 \color{red}{ +14x } \\\Leftrightarrow & 11x \color{red}{-15}\color{blue}{+15-14x } & = & 6 \color{red}{ +14x }\color{blue}{+15-14x } \\\Leftrightarrow & 11x \color{blue}{-14x } & = & 6 \color{blue}{+15} \\\Leftrightarrow &-3x & = &21\\\Leftrightarrow & \color{red}{-3}x & = &21\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{21}{-3} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)