Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{+2}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+2}\color{blue}{-2-x } & = & -12 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -12 \color{blue}{-2} \\\Leftrightarrow &x & = &-14\\\Leftrightarrow & \color{red}{}x & = &-14\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -14 \\\Leftrightarrow & \color{green}{ x = -14 } & & \\ & V = \left\{ -14 \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{+6}& = & 8 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{+6}\color{blue}{-6+15x } & = & 8 \color{red}{ -15x }\color{blue}{-6+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & 8 \color{blue}{-6} \\\Leftrightarrow &23x & = &2\\\Leftrightarrow & \color{red}{23}x & = &2\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{2}{23} \\\Leftrightarrow & \color{green}{ x = \frac{2}{23} } & & \\ & V = \left\{ \frac{2}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{+7}& = & -3 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{+7}\color{blue}{-7+3x } & = & -3 \color{red}{ -3x }\color{blue}{-7+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & -3 \color{blue}{-7} \\\Leftrightarrow &7x & = &-10\\\Leftrightarrow & \color{red}{7}x & = &-10\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-10}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{7} } & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{+7}& = & -8 \color{red}{ +13x } \\\Leftrightarrow & 11x \color{red}{+7}\color{blue}{-7-13x } & = & -8 \color{red}{ +13x }\color{blue}{-7-13x } \\\Leftrightarrow & 11x \color{blue}{-13x } & = & -8 \color{blue}{-7} \\\Leftrightarrow &-2x & = &-15\\\Leftrightarrow & \color{red}{-2}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-15}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{15}{2} } & & \\ & V = \left\{ \frac{15}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{-8}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-8}\color{blue}{+8-7x } & = & -7 \color{red}{ +7x }\color{blue}{+8-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -7 \color{blue}{+8} \\\Leftrightarrow &-13x & = &1\\\Leftrightarrow & \color{red}{-13}x & = &1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{+2}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{+2}\color{blue}{-2-x } & = & -9 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & -9 \color{blue}{-2} \\\Leftrightarrow &12x & = &-11\\\Leftrightarrow & \color{red}{12}x & = &-11\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-11}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{12} } & & \\ & V = \left\{ \frac{-11}{12} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{+12}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+12}\color{blue}{-12-x } & = & -10 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -10 \color{blue}{-12} \\\Leftrightarrow &-12x & = &-22\\\Leftrightarrow & \color{red}{-12}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-22}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{11}{6} } & & \\ & V = \left\{ \frac{11}{6} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{-5}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-5}\color{blue}{+5-x } & = & -7 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -7 \color{blue}{+5} \\\Leftrightarrow &-10x & = &-2\\\Leftrightarrow & \color{red}{-10}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-2}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{+14}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+14}\color{blue}{-14-x } & = & -10 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -10 \color{blue}{-14} \\\Leftrightarrow &-12x & = &-24\\\Leftrightarrow & \color{red}{-12}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-24}{-12} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{+15}& = & -5 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{+15}\color{blue}{-15+10x } & = & -5 \color{red}{ -10x }\color{blue}{-15+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & -5 \color{blue}{-15} \\\Leftrightarrow &21x & = &-20\\\Leftrightarrow & \color{red}{21}x & = &-20\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{-20}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{21} } & & \\ & V = \left\{ \frac{-20}{21} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{+1}& = & 10 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+1}\color{blue}{-1+7x } & = & 10 \color{red}{ -7x }\color{blue}{-1+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & 10 \color{blue}{-1} \\\Leftrightarrow &11x & = &9\\\Leftrightarrow & \color{red}{11}x & = &9\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{9}{11} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{-12}& = & 12 \color{red}{ +9x } \\\Leftrightarrow & -x \color{red}{-12}\color{blue}{+12-9x } & = & 12 \color{red}{ +9x }\color{blue}{+12-9x } \\\Leftrightarrow & -x \color{blue}{-9x } & = & 12 \color{blue}{+12} \\\Leftrightarrow &-10x & = &24\\\Leftrightarrow & \color{red}{-10}x & = &24\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{24}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{5} } & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)