Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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