Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{+14}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+14}\color{blue}{-14-x } & = & 4 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 4 \color{blue}{-14} \\\Leftrightarrow &13x & = &-10\\\Leftrightarrow & \color{red}{13}x & = &-10\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-10}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{13} } & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{-14}& = & -4 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{-14}\color{blue}{+14+15x } & = & -4 \color{red}{ -15x }\color{blue}{+14+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & -4 \color{blue}{+14} \\\Leftrightarrow &19x & = &10\\\Leftrightarrow & \color{red}{19}x & = &10\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{10}{19} \\\Leftrightarrow & \color{green}{ x = \frac{10}{19} } & & \\ & V = \left\{ \frac{10}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{+3}& = & 9 \color{red}{ +11x } \\\Leftrightarrow & 9x \color{red}{+3}\color{blue}{-3-11x } & = & 9 \color{red}{ +11x }\color{blue}{-3-11x } \\\Leftrightarrow & 9x \color{blue}{-11x } & = & 9 \color{blue}{-3} \\\Leftrightarrow &-2x & = &6\\\Leftrightarrow & \color{red}{-2}x & = &6\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{6}{-2} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{-10}& = & -9 \color{red}{ -15x } \\\Leftrightarrow & -x \color{red}{-10}\color{blue}{+10+15x } & = & -9 \color{red}{ -15x }\color{blue}{+10+15x } \\\Leftrightarrow & -x \color{blue}{+15x } & = & -9 \color{blue}{+10} \\\Leftrightarrow &14x & = &1\\\Leftrightarrow & \color{red}{14}x & = &1\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{1}{14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{14} } & & \\ & V = \left\{ \frac{1}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{-14}& = & 2 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{-14}\color{blue}{+14-5x } & = & 2 \color{red}{ +5x }\color{blue}{+14-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & 2 \color{blue}{+14} \\\Leftrightarrow &x & = &16\\\Leftrightarrow & \color{red}{}x & = &16\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 16 \\\Leftrightarrow & \color{green}{ x = 16 } & & \\ & V = \left\{ 16 \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{+4}& = & -14 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+4}\color{blue}{-4-13x } & = & -14 \color{red}{ +13x }\color{blue}{-4-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -14 \color{blue}{-4} \\\Leftrightarrow &-25x & = &-18\\\Leftrightarrow & \color{red}{-25}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-18}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{18}{25} } & & \\ & V = \left\{ \frac{18}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{-15}& = & 10 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-15}\color{blue}{+15-13x } & = & 10 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 10 \color{blue}{+15} \\\Leftrightarrow &-19x & = &25\\\Leftrightarrow & \color{red}{-19}x & = &25\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{25}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{19} } & & \\ & V = \left\{ \frac{-25}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{-9}& = & -4 \color{red}{ +5x } \\\Leftrightarrow & 11x \color{red}{-9}\color{blue}{+9-5x } & = & -4 \color{red}{ +5x }\color{blue}{+9-5x } \\\Leftrightarrow & 11x \color{blue}{-5x } & = & -4 \color{blue}{+9} \\\Leftrightarrow &6x & = &5\\\Leftrightarrow & \color{red}{6}x & = &5\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{5}{6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{+15}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+15}\color{blue}{-15-x } & = & -5 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -5 \color{blue}{-15} \\\Leftrightarrow &-13x & = &-20\\\Leftrightarrow & \color{red}{-13}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-20}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{20}{13} } & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & x \color{red}{-12}& = & 4 \color{red}{ +13x } \\\Leftrightarrow & x \color{red}{-12}\color{blue}{+12-13x } & = & 4 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & x \color{blue}{-13x } & = & 4 \color{blue}{+12} \\\Leftrightarrow &-12x & = &16\\\Leftrightarrow & \color{red}{-12}x & = &16\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{16}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{+1}& = & -7 \color{red}{ +5x } \\\Leftrightarrow & -14x \color{red}{+1}\color{blue}{-1-5x } & = & -7 \color{red}{ +5x }\color{blue}{-1-5x } \\\Leftrightarrow & -14x \color{blue}{-5x } & = & -7 \color{blue}{-1} \\\Leftrightarrow &-19x & = &-8\\\Leftrightarrow & \color{red}{-19}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-8}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{8}{19} } & & \\ & V = \left\{ \frac{8}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{-4}& = & -3 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-4}\color{blue}{+4-13x } & = & -3 \color{red}{ +13x }\color{blue}{+4-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -3 \color{blue}{+4} \\\Leftrightarrow &-25x & = &1\\\Leftrightarrow & \color{red}{-25}x & = &1\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{1}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{25} } & & \\ & V = \left\{ \frac{-1}{25} \right\} & \\\end{align}\)