Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{+15}& = & 15 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{+15}\color{blue}{-15-7x } & = & 15 \color{red}{ +7x }\color{blue}{-15-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & 15 \color{blue}{-15} \\\Leftrightarrow &-5x & = &0\\\Leftrightarrow & \color{red}{-5}x & = &0\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{0}{-5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{+6}& = & 15 \color{red}{ +13x } \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6-13x } & = & 15 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & 15x \color{blue}{-13x } & = & 15 \color{blue}{-6} \\\Leftrightarrow &2x & = &9\\\Leftrightarrow & \color{red}{2}x & = &9\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{9}{2} \\\Leftrightarrow & \color{green}{ x = \frac{9}{2} } & & \\ & V = \left\{ \frac{9}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{-1}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-1}\color{blue}{+1-x } & = & 15 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 15 \color{blue}{+1} \\\Leftrightarrow &-6x & = &16\\\Leftrightarrow & \color{red}{-6}x & = &16\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{16}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{-15}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{-15}\color{blue}{+15-x } & = & 3 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & 3 \color{blue}{+15} \\\Leftrightarrow &12x & = &18\\\Leftrightarrow & \color{red}{12}x & = &18\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{18}{12} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{+14}& = & -3 \color{red}{ +2x } \\\Leftrightarrow & 9x \color{red}{+14}\color{blue}{-14-2x } & = & -3 \color{red}{ +2x }\color{blue}{-14-2x } \\\Leftrightarrow & 9x \color{blue}{-2x } & = & -3 \color{blue}{-14} \\\Leftrightarrow &7x & = &-17\\\Leftrightarrow & \color{red}{7}x & = &-17\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-17}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{7} } & & \\ & V = \left\{ \frac{-17}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{+5}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+5}\color{blue}{-5-x } & = & -1 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -1 \color{blue}{-5} \\\Leftrightarrow &-12x & = &-6\\\Leftrightarrow & \color{red}{-12}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-6}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{+4}& = & 11 \color{red}{ +4x } \\\Leftrightarrow & 15x \color{red}{+4}\color{blue}{-4-4x } & = & 11 \color{red}{ +4x }\color{blue}{-4-4x } \\\Leftrightarrow & 15x \color{blue}{-4x } & = & 11 \color{blue}{-4} \\\Leftrightarrow &11x & = &7\\\Leftrightarrow & \color{red}{11}x & = &7\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{7}{11} \\\Leftrightarrow & \color{green}{ x = \frac{7}{11} } & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{+10}& = & -2 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{+10}\color{blue}{-10-6x } & = & -2 \color{red}{ +6x }\color{blue}{-10-6x } \\\Leftrightarrow & -11x \color{blue}{-6x } & = & -2 \color{blue}{-10} \\\Leftrightarrow &-17x & = &-12\\\Leftrightarrow & \color{red}{-17}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-12}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{12}{17} } & & \\ & V = \left\{ \frac{12}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{-15}& = & -14 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-15}\color{blue}{+15-9x } & = & -14 \color{red}{ +9x }\color{blue}{+15-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -14 \color{blue}{+15} \\\Leftrightarrow &-17x & = &1\\\Leftrightarrow & \color{red}{-17}x & = &1\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{1}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{17} } & & \\ & V = \left\{ \frac{-1}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{-12}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-12}\color{blue}{+12-x } & = & 2 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 2 \color{blue}{+12} \\\Leftrightarrow &-12x & = &14\\\Leftrightarrow & \color{red}{-12}x & = &14\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{14}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{6} } & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{-7}& = & -14 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{-7}\color{blue}{+7-9x } & = & -14 \color{red}{ +9x }\color{blue}{+7-9x } \\\Leftrightarrow & 4x \color{blue}{-9x } & = & -14 \color{blue}{+7} \\\Leftrightarrow &-5x & = &-7\\\Leftrightarrow & \color{red}{-5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{+3}& = & -1 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{+3}\color{blue}{-3+6x } & = & -1 \color{red}{ -6x }\color{blue}{-3+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & -1 \color{blue}{-3} \\\Leftrightarrow &13x & = &-4\\\Leftrightarrow & \color{red}{13}x & = &-4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)