Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{-6}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-6}\color{blue}{+6-x } & = & -1 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -1 \color{blue}{+6} \\\Leftrightarrow &-10x & = &5\\\Leftrightarrow & \color{red}{-10}x & = &5\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{5}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{+15}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+15}\color{blue}{-15-x } & = & -10 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -10 \color{blue}{-15} \\\Leftrightarrow &-6x & = &-25\\\Leftrightarrow & \color{red}{-6}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-25}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{25}{6} } & & \\ & V = \left\{ \frac{25}{6} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{-9}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-9}\color{blue}{+9-x } & = & 13 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 13 \color{blue}{+9} \\\Leftrightarrow &-14x & = &22\\\Leftrightarrow & \color{red}{-14}x & = &22\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{22}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{7} } & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{-14}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{-14}\color{blue}{+14-x } & = & 6 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & 6 \color{blue}{+14} \\\Leftrightarrow &10x & = &20\\\Leftrightarrow & \color{red}{10}x & = &20\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{20}{10} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{+14}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & 2x \color{red}{+14}\color{blue}{-14-13x } & = & 9 \color{red}{ +13x }\color{blue}{-14-13x } \\\Leftrightarrow & 2x \color{blue}{-13x } & = & 9 \color{blue}{-14} \\\Leftrightarrow &-11x & = &-5\\\Leftrightarrow & \color{red}{-11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{+1}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+1}\color{blue}{-1-x } & = & 2 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 2 \color{blue}{-1} \\\Leftrightarrow &-12x & = &1\\\Leftrightarrow & \color{red}{-12}x & = &1\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{1}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{12} } & & \\ & V = \left\{ \frac{-1}{12} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{-3}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-3}\color{blue}{+3-x } & = & -2 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -2 \color{blue}{+3} \\\Leftrightarrow &-16x & = &1\\\Leftrightarrow & \color{red}{-16}x & = &1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{16} } & & \\ & V = \left\{ \frac{-1}{16} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{+7}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+7}\color{blue}{-7-x } & = & 12 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 12 \color{blue}{-7} \\\Leftrightarrow &-9x & = &5\\\Leftrightarrow & \color{red}{-9}x & = &5\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{5}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{9} } & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{-14}& = & -3 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{-14}\color{blue}{+14+10x } & = & -3 \color{red}{ -10x }\color{blue}{+14+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & -3 \color{blue}{+14} \\\Leftrightarrow &17x & = &11\\\Leftrightarrow & \color{red}{17}x & = &11\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{11}{17} \\\Leftrightarrow & \color{green}{ x = \frac{11}{17} } & & \\ & V = \left\{ \frac{11}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{-5}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-5}\color{blue}{+5-x } & = & -1 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -1 \color{blue}{+5} \\\Leftrightarrow &-13x & = &4\\\Leftrightarrow & \color{red}{-13}x & = &4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{-2}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-2}\color{blue}{+2-x } & = & 12 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 12 \color{blue}{+2} \\\Leftrightarrow &5x & = &14\\\Leftrightarrow & \color{red}{5}x & = &14\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{14}{5} \\\Leftrightarrow & \color{green}{ x = \frac{14}{5} } & & \\ & V = \left\{ \frac{14}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{+10}& = & 3 \color{red}{ +8x } \\\Leftrightarrow & -5x \color{red}{+10}\color{blue}{-10-8x } & = & 3 \color{red}{ +8x }\color{blue}{-10-8x } \\\Leftrightarrow & -5x \color{blue}{-8x } & = & 3 \color{blue}{-10} \\\Leftrightarrow &-13x & = &-7\\\Leftrightarrow & \color{red}{-13}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)