Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{-9}& = & -4 \color{red}{ +13x } \\\Leftrightarrow & 14x \color{red}{-9}\color{blue}{+9-13x } & = & -4 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & 14x \color{blue}{-13x } & = & -4 \color{blue}{+9} \\\Leftrightarrow &x & = &5\\\Leftrightarrow & \color{red}{}x & = &5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 5 \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{+14}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+14}\color{blue}{-14-x } & = & 4 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 4 \color{blue}{-14} \\\Leftrightarrow &-12x & = &-10\\\Leftrightarrow & \color{red}{-12}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-10}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{+5}& = & 3 \color{red}{ +12x } \\\Leftrightarrow & x \color{red}{+5}\color{blue}{-5-12x } & = & 3 \color{red}{ +12x }\color{blue}{-5-12x } \\\Leftrightarrow & x \color{blue}{-12x } & = & 3 \color{blue}{-5} \\\Leftrightarrow &-11x & = &-2\\\Leftrightarrow & \color{red}{-11}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-8}& = & -2 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-8}\color{blue}{+8-13x } & = & -2 \color{red}{ +13x }\color{blue}{+8-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -2 \color{blue}{+8} \\\Leftrightarrow &-28x & = &6\\\Leftrightarrow & \color{red}{-28}x & = &6\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{6}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{14} } & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{-11}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-11}\color{blue}{+11-x } & = & -8 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -8 \color{blue}{+11} \\\Leftrightarrow &7x & = &3\\\Leftrightarrow & \color{red}{7}x & = &3\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{3}{7} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{+6}& = & 1 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{+6}\color{blue}{-6+12x } & = & 1 \color{red}{ -12x }\color{blue}{-6+12x } \\\Leftrightarrow & 5x \color{blue}{+12x } & = & 1 \color{blue}{-6} \\\Leftrightarrow &17x & = &-5\\\Leftrightarrow & \color{red}{17}x & = &-5\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-5}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{17} } & & \\ & V = \left\{ \frac{-5}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{+5}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+5}\color{blue}{-5-x } & = & -15 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -15 \color{blue}{-5} \\\Leftrightarrow &-4x & = &-20\\\Leftrightarrow & \color{red}{-4}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-20}{-4} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{-15}& = & -3 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{-15}\color{blue}{+15-13x } & = & -3 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & -3 \color{blue}{+15} \\\Leftrightarrow &-16x & = &12\\\Leftrightarrow & \color{red}{-16}x & = &12\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{12}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{+15}& = & -9 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{+15}\color{blue}{-15-11x } & = & -9 \color{red}{ +11x }\color{blue}{-15-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & -9 \color{blue}{-15} \\\Leftrightarrow &-5x & = &-24\\\Leftrightarrow & \color{red}{-5}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-24}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{24}{5} } & & \\ & V = \left\{ \frac{24}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{+14}& = & 13 \color{red}{ -3x } \\\Leftrightarrow & 13x \color{red}{+14}\color{blue}{-14+3x } & = & 13 \color{red}{ -3x }\color{blue}{-14+3x } \\\Leftrightarrow & 13x \color{blue}{+3x } & = & 13 \color{blue}{-14} \\\Leftrightarrow &16x & = &-1\\\Leftrightarrow & \color{red}{16}x & = &-1\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-1}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{16} } & & \\ & V = \left\{ \frac{-1}{16} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{+8}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+8}\color{blue}{-8-x } & = & 11 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 11 \color{blue}{-8} \\\Leftrightarrow &-15x & = &3\\\Leftrightarrow & \color{red}{-15}x & = &3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 3x \color{red}{-11}& = & -1 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{-11}\color{blue}{+11+11x } & = & -1 \color{red}{ -11x }\color{blue}{+11+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & -1 \color{blue}{+11} \\\Leftrightarrow &14x & = &10\\\Leftrightarrow & \color{red}{14}x & = &10\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{10}{14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)