Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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