Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{+12}& = & -2 \color{red}{ +13x } \\\Leftrightarrow & 6x \color{red}{+12}\color{blue}{-12-13x } & = & -2 \color{red}{ +13x }\color{blue}{-12-13x } \\\Leftrightarrow & 6x \color{blue}{-13x } & = & -2 \color{blue}{-12} \\\Leftrightarrow &-7x & = &-14\\\Leftrightarrow & \color{red}{-7}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-14}{-7} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{-2}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-2}\color{blue}{+2-x } & = & -2 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -2 \color{blue}{+2} \\\Leftrightarrow &-15x & = &0\\\Leftrightarrow & \color{red}{-15}x & = &0\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{0}{-15} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{-6}& = & 7 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{-6}\color{blue}{+6+13x } & = & 7 \color{red}{ -13x }\color{blue}{+6+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & 7 \color{blue}{+6} \\\Leftrightarrow &20x & = &13\\\Leftrightarrow & \color{red}{20}x & = &13\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{13}{20} \\\Leftrightarrow & \color{green}{ x = \frac{13}{20} } & & \\ & V = \left\{ \frac{13}{20} \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{-1}& = & -1 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{-1}\color{blue}{+1-9x } & = & -1 \color{red}{ +9x }\color{blue}{+1-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & -1 \color{blue}{+1} \\\Leftrightarrow &-x & = &0\\\Leftrightarrow & \color{red}{-}x & = &0\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{0}{-1} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & -10x \color{red}{-5}& = & 6 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-5}\color{blue}{+5-7x } & = & 6 \color{red}{ +7x }\color{blue}{+5-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 6 \color{blue}{+5} \\\Leftrightarrow &-17x & = &11\\\Leftrightarrow & \color{red}{-17}x & = &11\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{11}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{17} } & & \\ & V = \left\{ \frac{-11}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{-5}& = & -14 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-5}\color{blue}{+5-7x } & = & -14 \color{red}{ +7x }\color{blue}{+5-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -14 \color{blue}{+5} \\\Leftrightarrow &-13x & = &-9\\\Leftrightarrow & \color{red}{-13}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-9}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{9}{13} } & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{+5}& = & 11 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+5}\color{blue}{-5+11x } & = & 11 \color{red}{ -11x }\color{blue}{-5+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & 11 \color{blue}{-5} \\\Leftrightarrow &15x & = &6\\\Leftrightarrow & \color{red}{15}x & = &6\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{6}{15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{-8}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-8}\color{blue}{+8-x } & = & 1 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 1 \color{blue}{+8} \\\Leftrightarrow &-14x & = &9\\\Leftrightarrow & \color{red}{-14}x & = &9\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{9}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{14} } & & \\ & V = \left\{ \frac{-9}{14} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{-14}& = & -4 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{-14}\color{blue}{+14-8x } & = & -4 \color{red}{ +8x }\color{blue}{+14-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & -4 \color{blue}{+14} \\\Leftrightarrow &-23x & = &10\\\Leftrightarrow & \color{red}{-23}x & = &10\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{10}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{23} } & & \\ & V = \left\{ \frac{-10}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{+6}& = & 13 \color{red}{ +9x } \\\Leftrightarrow & 13x \color{red}{+6}\color{blue}{-6-9x } & = & 13 \color{red}{ +9x }\color{blue}{-6-9x } \\\Leftrightarrow & 13x \color{blue}{-9x } & = & 13 \color{blue}{-6} \\\Leftrightarrow &4x & = &7\\\Leftrightarrow & \color{red}{4}x & = &7\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{7}{4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & 2x \color{red}{+2}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+2}\color{blue}{-2-x } & = & 9 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 9 \color{blue}{-2} \\\Leftrightarrow &x & = &7\\\Leftrightarrow & \color{red}{}x & = &7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 7 \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{-4}& = & 4 \color{red}{ -4x } \\\Leftrightarrow & x \color{red}{-4}\color{blue}{+4+4x } & = & 4 \color{red}{ -4x }\color{blue}{+4+4x } \\\Leftrightarrow & x \color{blue}{+4x } & = & 4 \color{blue}{+4} \\\Leftrightarrow &5x & = &8\\\Leftrightarrow & \color{red}{5}x & = &8\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{8}{5} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)