Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{-10}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-10}\color{blue}{+10-x } & = & 5 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 5 \color{blue}{+10} \\\Leftrightarrow &-7x & = &15\\\Leftrightarrow & \color{red}{-7}x & = &15\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{15}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{7} } & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-12}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-12}\color{blue}{+12-x } & = & -14 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -14 \color{blue}{+12} \\\Leftrightarrow &11x & = &-2\\\Leftrightarrow & \color{red}{11}x & = &-2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{-15}& = & -8 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{-15}\color{blue}{+15+4x } & = & -8 \color{red}{ -4x }\color{blue}{+15+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -8 \color{blue}{+15} \\\Leftrightarrow &13x & = &7\\\Leftrightarrow & \color{red}{13}x & = &7\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{7}{13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{-4}& = & 5 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-4}\color{blue}{+4-13x } & = & 5 \color{red}{ +13x }\color{blue}{+4-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 5 \color{blue}{+4} \\\Leftrightarrow &-19x & = &9\\\Leftrightarrow & \color{red}{-19}x & = &9\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{9}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{19} } & & \\ & V = \left\{ \frac{-9}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{-6}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-6}\color{blue}{+6-x } & = & -3 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -3 \color{blue}{+6} \\\Leftrightarrow &x & = &3\\\Leftrightarrow & \color{red}{}x & = &3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 3 \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{-8}& = & 6 \color{red}{ +13x } \\\Leftrightarrow & 2x \color{red}{-8}\color{blue}{+8-13x } & = & 6 \color{red}{ +13x }\color{blue}{+8-13x } \\\Leftrightarrow & 2x \color{blue}{-13x } & = & 6 \color{blue}{+8} \\\Leftrightarrow &-11x & = &14\\\Leftrightarrow & \color{red}{-11}x & = &14\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{14}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{11} } & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{-15}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-15}\color{blue}{+15-x } & = & 10 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 10 \color{blue}{+15} \\\Leftrightarrow &11x & = &25\\\Leftrightarrow & \color{red}{11}x & = &25\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{25}{11} \\\Leftrightarrow & \color{green}{ x = \frac{25}{11} } & & \\ & V = \left\{ \frac{25}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{-11}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-11}\color{blue}{+11-x } & = & -10 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -10 \color{blue}{+11} \\\Leftrightarrow &-11x & = &1\\\Leftrightarrow & \color{red}{-11}x & = &1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{-15}& = & -1 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-15}\color{blue}{+15+3x } & = & -1 \color{red}{ -3x }\color{blue}{+15+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -1 \color{blue}{+15} \\\Leftrightarrow &13x & = &14\\\Leftrightarrow & \color{red}{13}x & = &14\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{14}{13} \\\Leftrightarrow & \color{green}{ x = \frac{14}{13} } & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{-15}& = & -15 \color{red}{ +3x } \\\Leftrightarrow & 8x \color{red}{-15}\color{blue}{+15-3x } & = & -15 \color{red}{ +3x }\color{blue}{+15-3x } \\\Leftrightarrow & 8x \color{blue}{-3x } & = & -15 \color{blue}{+15} \\\Leftrightarrow &5x & = &0\\\Leftrightarrow & \color{red}{5}x & = &0\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{0}{5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{+2}& = & -10 \color{red}{ +7x } \\\Leftrightarrow & x \color{red}{+2}\color{blue}{-2-7x } & = & -10 \color{red}{ +7x }\color{blue}{-2-7x } \\\Leftrightarrow & x \color{blue}{-7x } & = & -10 \color{blue}{-2} \\\Leftrightarrow &-6x & = &-12\\\Leftrightarrow & \color{red}{-6}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-12}{-6} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{+6}& = & 2 \color{red}{ -2x } \\\Leftrightarrow & 9x \color{red}{+6}\color{blue}{-6+2x } & = & 2 \color{red}{ -2x }\color{blue}{-6+2x } \\\Leftrightarrow & 9x \color{blue}{+2x } & = & 2 \color{blue}{-6} \\\Leftrightarrow &11x & = &-4\\\Leftrightarrow & \color{red}{11}x & = &-4\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-4}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)