Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{+9}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+9}\color{blue}{-9-x } & = & -10 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -10 \color{blue}{-9} \\\Leftrightarrow &-15x & = &-19\\\Leftrightarrow & \color{red}{-15}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-19}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{19}{15} } & & \\ & V = \left\{ \frac{19}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{+5}& = & 14 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+5}\color{blue}{-5-x } & = & 14 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 14 \color{blue}{-5} \\\Leftrightarrow &5x & = &9\\\Leftrightarrow & \color{red}{5}x & = &9\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{9}{5} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{-5}& = & -14 \color{red}{ -9x } \\\Leftrightarrow & 14x \color{red}{-5}\color{blue}{+5+9x } & = & -14 \color{red}{ -9x }\color{blue}{+5+9x } \\\Leftrightarrow & 14x \color{blue}{+9x } & = & -14 \color{blue}{+5} \\\Leftrightarrow &23x & = &-9\\\Leftrightarrow & \color{red}{23}x & = &-9\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-9}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{23} } & & \\ & V = \left\{ \frac{-9}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{+2}& = & 11 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{+2}\color{blue}{-2+3x } & = & 11 \color{red}{ -3x }\color{blue}{-2+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & 11 \color{blue}{-2} \\\Leftrightarrow &7x & = &9\\\Leftrightarrow & \color{red}{7}x & = &9\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{9}{7} \\\Leftrightarrow & \color{green}{ x = \frac{9}{7} } & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{+15}& = & -15 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{+15}\color{blue}{-15-13x } & = & -15 \color{red}{ +13x }\color{blue}{-15-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & -15 \color{blue}{-15} \\\Leftrightarrow &-3x & = &-30\\\Leftrightarrow & \color{red}{-3}x & = &-30\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-30}{-3} \\\Leftrightarrow & \color{green}{ x = 10 } & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{+14}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+14}\color{blue}{-14-x } & = & -11 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -11 \color{blue}{-14} \\\Leftrightarrow &-13x & = &-25\\\Leftrightarrow & \color{red}{-13}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-25}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{25}{13} } & & \\ & V = \left\{ \frac{25}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 6x \color{red}{-3}& = & 7 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-3}\color{blue}{+3+11x } & = & 7 \color{red}{ -11x }\color{blue}{+3+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 7 \color{blue}{+3} \\\Leftrightarrow &17x & = &10\\\Leftrightarrow & \color{red}{17}x & = &10\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{10}{17} \\\Leftrightarrow & \color{green}{ x = \frac{10}{17} } & & \\ & V = \left\{ \frac{10}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{+4}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+4}\color{blue}{-4-13x } & = & 3 \color{red}{ +13x }\color{blue}{-4-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 3 \color{blue}{-4} \\\Leftrightarrow &-25x & = &-1\\\Leftrightarrow & \color{red}{-25}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-1}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{1}{25} } & & \\ & V = \left\{ \frac{1}{25} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{+13}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+13}\color{blue}{-13-x } & = & 4 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 4 \color{blue}{-13} \\\Leftrightarrow &-3x & = &-9\\\Leftrightarrow & \color{red}{-3}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-9}{-3} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{-6}& = & -10 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-6}\color{blue}{+6-9x } & = & -10 \color{red}{ +9x }\color{blue}{+6-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & -10 \color{blue}{+6} \\\Leftrightarrow &5x & = &-4\\\Leftrightarrow & \color{red}{5}x & = &-4\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-4}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{+15}& = & 13 \color{red}{ +9x } \\\Leftrightarrow & -2x \color{red}{+15}\color{blue}{-15-9x } & = & 13 \color{red}{ +9x }\color{blue}{-15-9x } \\\Leftrightarrow & -2x \color{blue}{-9x } & = & 13 \color{blue}{-15} \\\Leftrightarrow &-11x & = &-2\\\Leftrightarrow & \color{red}{-11}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{+9}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+9}\color{blue}{-9-x } & = & 1 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 1 \color{blue}{-9} \\\Leftrightarrow &13x & = &-8\\\Leftrightarrow & \color{red}{13}x & = &-8\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-8}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{13} } & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)