Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{-6}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-6}\color{blue}{+6-x } & = & 15 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 15 \color{blue}{+6} \\\Leftrightarrow &-5x & = &21\\\Leftrightarrow & \color{red}{-5}x & = &21\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{21}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{5} } & & \\ & V = \left\{ \frac{-21}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-12}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-12}\color{blue}{+12-x } & = & -2 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -2 \color{blue}{+12} \\\Leftrightarrow &11x & = &10\\\Leftrightarrow & \color{red}{11}x & = &10\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{10}{11} \\\Leftrightarrow & \color{green}{ x = \frac{10}{11} } & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{-12}& = & 12 \color{red}{ -5x } \\\Leftrightarrow & -x \color{red}{-12}\color{blue}{+12+5x } & = & 12 \color{red}{ -5x }\color{blue}{+12+5x } \\\Leftrightarrow & -x \color{blue}{+5x } & = & 12 \color{blue}{+12} \\\Leftrightarrow &4x & = &24\\\Leftrightarrow & \color{red}{4}x & = &24\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{24}{4} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{+8}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+8}\color{blue}{-8-x } & = & 4 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 4 \color{blue}{-8} \\\Leftrightarrow &-11x & = &-4\\\Leftrightarrow & \color{red}{-11}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-4}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{4}{11} } & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{+4}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+4}\color{blue}{-4-x } & = & 3 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 3 \color{blue}{-4} \\\Leftrightarrow &-14x & = &-1\\\Leftrightarrow & \color{red}{-14}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-1}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{14} } & & \\ & V = \left\{ \frac{1}{14} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{-12}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-12}\color{blue}{+12-x } & = & 10 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 10 \color{blue}{+12} \\\Leftrightarrow &-6x & = &22\\\Leftrightarrow & \color{red}{-6}x & = &22\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{22}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{+2}& = & 14 \color{red}{ +8x } \\\Leftrightarrow & -5x \color{red}{+2}\color{blue}{-2-8x } & = & 14 \color{red}{ +8x }\color{blue}{-2-8x } \\\Leftrightarrow & -5x \color{blue}{-8x } & = & 14 \color{blue}{-2} \\\Leftrightarrow &-13x & = &12\\\Leftrightarrow & \color{red}{-13}x & = &12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{-12}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & 7x \color{red}{-12}\color{blue}{+12-13x } & = & 3 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & 7x \color{blue}{-13x } & = & 3 \color{blue}{+12} \\\Leftrightarrow &-6x & = &15\\\Leftrightarrow & \color{red}{-6}x & = &15\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{15}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{-6}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-6}\color{blue}{+6-x } & = & -8 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -8 \color{blue}{+6} \\\Leftrightarrow &-12x & = &-2\\\Leftrightarrow & \color{red}{-12}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-2}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{+14}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+14}\color{blue}{-14-x } & = & -4 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -4 \color{blue}{-14} \\\Leftrightarrow &-15x & = &-18\\\Leftrightarrow & \color{red}{-15}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-18}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{-8}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8-13x } & = & 14 \color{red}{ +13x }\color{blue}{+8-13x } \\\Leftrightarrow & 14x \color{blue}{-13x } & = & 14 \color{blue}{+8} \\\Leftrightarrow &x & = &22\\\Leftrightarrow & \color{red}{}x & = &22\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 22 \\\Leftrightarrow & \color{green}{ x = 22 } & & \\ & V = \left\{ 22 \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{+11}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+11}\color{blue}{-11-x } & = & 13 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 13 \color{blue}{-11} \\\Leftrightarrow &-10x & = &2\\\Leftrightarrow & \color{red}{-10}x & = &2\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{2}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)