Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{-13}& = & -2 \color{red}{ -5x } \\\Leftrightarrow & x \color{red}{-13}\color{blue}{+13+5x } & = & -2 \color{red}{ -5x }\color{blue}{+13+5x } \\\Leftrightarrow & x \color{blue}{+5x } & = & -2 \color{blue}{+13} \\\Leftrightarrow &6x & = &11\\\Leftrightarrow & \color{red}{6}x & = &11\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{11}{6} \\\Leftrightarrow & \color{green}{ x = \frac{11}{6} } & & \\ & V = \left\{ \frac{11}{6} \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{-6}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-6}\color{blue}{+6-x } & = & -3 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -3 \color{blue}{+6} \\\Leftrightarrow &-13x & = &3\\\Leftrightarrow & \color{red}{-13}x & = &3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{+7}& = & 7 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+7}\color{blue}{-7-5x } & = & 7 \color{red}{ +5x }\color{blue}{-7-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & 7 \color{blue}{-7} \\\Leftrightarrow &-14x & = &0\\\Leftrightarrow & \color{red}{-14}x & = &0\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{0}{-14} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{-6}& = & -15 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{-6}\color{blue}{+6+7x } & = & -15 \color{red}{ -7x }\color{blue}{+6+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & -15 \color{blue}{+6} \\\Leftrightarrow &19x & = &-9\\\Leftrightarrow & \color{red}{19}x & = &-9\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-9}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{19} } & & \\ & V = \left\{ \frac{-9}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{-15}& = & 1 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{-15}\color{blue}{+15-5x } & = & 1 \color{red}{ +5x }\color{blue}{+15-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & 1 \color{blue}{+15} \\\Leftrightarrow &7x & = &16\\\Leftrightarrow & \color{red}{7}x & = &16\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{16}{7} \\\Leftrightarrow & \color{green}{ x = \frac{16}{7} } & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{-5}& = & 2 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{-5}\color{blue}{+5+12x } & = & 2 \color{red}{ -12x }\color{blue}{+5+12x } \\\Leftrightarrow & 5x \color{blue}{+12x } & = & 2 \color{blue}{+5} \\\Leftrightarrow &17x & = &7\\\Leftrightarrow & \color{red}{17}x & = &7\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{7}{17} \\\Leftrightarrow & \color{green}{ x = \frac{7}{17} } & & \\ & V = \left\{ \frac{7}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{+12}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+12}\color{blue}{-12-x } & = & 10 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 10 \color{blue}{-12} \\\Leftrightarrow &-11x & = &-2\\\Leftrightarrow & \color{red}{-11}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{+7}& = & 13 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+7}\color{blue}{-7+3x } & = & 13 \color{red}{ -3x }\color{blue}{-7+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 13 \color{blue}{-7} \\\Leftrightarrow &13x & = &6\\\Leftrightarrow & \color{red}{13}x & = &6\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{6}{13} \\\Leftrightarrow & \color{green}{ x = \frac{6}{13} } & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{+14}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+14}\color{blue}{-14-x } & = & -2 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -2 \color{blue}{-14} \\\Leftrightarrow &-14x & = &-16\\\Leftrightarrow & \color{red}{-14}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-16}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{8}{7} } & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{-11}& = & 14 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{-11}\color{blue}{+11+13x } & = & 14 \color{red}{ -13x }\color{blue}{+11+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & 14 \color{blue}{+11} \\\Leftrightarrow &22x & = &25\\\Leftrightarrow & \color{red}{22}x & = &25\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{25}{22} \\\Leftrightarrow & \color{green}{ x = \frac{25}{22} } & & \\ & V = \left\{ \frac{25}{22} \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{+5}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+5}\color{blue}{-5-x } & = & -5 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -5 \color{blue}{-5} \\\Leftrightarrow &-12x & = &-10\\\Leftrightarrow & \color{red}{-12}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-10}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{+11}& = & -14 \color{red}{ +10x } \\\Leftrightarrow & -13x \color{red}{+11}\color{blue}{-11-10x } & = & -14 \color{red}{ +10x }\color{blue}{-11-10x } \\\Leftrightarrow & -13x \color{blue}{-10x } & = & -14 \color{blue}{-11} \\\Leftrightarrow &-23x & = &-25\\\Leftrightarrow & \color{red}{-23}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-25}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{25}{23} } & & \\ & V = \left\{ \frac{25}{23} \right\} & \\\end{align}\)