Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{-13}& = & -4 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-13}\color{blue}{+13-7x } & = & -4 \color{red}{ +7x }\color{blue}{+13-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -4 \color{blue}{+13} \\\Leftrightarrow &-13x & = &9\\\Leftrightarrow & \color{red}{-13}x & = &9\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{9}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{13} } & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{+7}& = & 7 \color{red}{ -2x } \\\Leftrightarrow & x \color{red}{+7}\color{blue}{-7+2x } & = & 7 \color{red}{ -2x }\color{blue}{-7+2x } \\\Leftrightarrow & x \color{blue}{+2x } & = & 7 \color{blue}{-7} \\\Leftrightarrow &3x & = &0\\\Leftrightarrow & \color{red}{3}x & = &0\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{0}{3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{+5}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & 9x \color{red}{+5}\color{blue}{-5-13x } & = & -7 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & 9x \color{blue}{-13x } & = & -7 \color{blue}{-5} \\\Leftrightarrow &-4x & = &-12\\\Leftrightarrow & \color{red}{-4}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-12}{-4} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{+8}& = & 13 \color{red}{ -7x } \\\Leftrightarrow & 11x \color{red}{+8}\color{blue}{-8+7x } & = & 13 \color{red}{ -7x }\color{blue}{-8+7x } \\\Leftrightarrow & 11x \color{blue}{+7x } & = & 13 \color{blue}{-8} \\\Leftrightarrow &18x & = &5\\\Leftrightarrow & \color{red}{18}x & = &5\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}} & = & \frac{5}{18} \\\Leftrightarrow & \color{green}{ x = \frac{5}{18} } & & \\ & V = \left\{ \frac{5}{18} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{+10}& = & 1 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{+10}\color{blue}{-10-5x } & = & 1 \color{red}{ +5x }\color{blue}{-10-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & 1 \color{blue}{-10} \\\Leftrightarrow &-17x & = &-9\\\Leftrightarrow & \color{red}{-17}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-9}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{9}{17} } & & \\ & V = \left\{ \frac{9}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{+12}& = & -2 \color{red}{ +5x } \\\Leftrightarrow & 11x \color{red}{+12}\color{blue}{-12-5x } & = & -2 \color{red}{ +5x }\color{blue}{-12-5x } \\\Leftrightarrow & 11x \color{blue}{-5x } & = & -2 \color{blue}{-12} \\\Leftrightarrow &6x & = &-14\\\Leftrightarrow & \color{red}{6}x & = &-14\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-14}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{-14}& = & 14 \color{red}{ +14x } \\\Leftrightarrow & 9x \color{red}{-14}\color{blue}{+14-14x } & = & 14 \color{red}{ +14x }\color{blue}{+14-14x } \\\Leftrightarrow & 9x \color{blue}{-14x } & = & 14 \color{blue}{+14} \\\Leftrightarrow &-5x & = &28\\\Leftrightarrow & \color{red}{-5}x & = &28\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{28}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-28}{5} } & & \\ & V = \left\{ \frac{-28}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{-2}& = & 9 \color{red}{ +4x } \\\Leftrightarrow & 9x \color{red}{-2}\color{blue}{+2-4x } & = & 9 \color{red}{ +4x }\color{blue}{+2-4x } \\\Leftrightarrow & 9x \color{blue}{-4x } & = & 9 \color{blue}{+2} \\\Leftrightarrow &5x & = &11\\\Leftrightarrow & \color{red}{5}x & = &11\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{11}{5} \\\Leftrightarrow & \color{green}{ x = \frac{11}{5} } & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{+5}& = & 6 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+5}\color{blue}{-5-7x } & = & 6 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 6 \color{blue}{-5} \\\Leftrightarrow &-17x & = &1\\\Leftrightarrow & \color{red}{-17}x & = &1\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{1}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{17} } & & \\ & V = \left\{ \frac{-1}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{-5}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{-5}\color{blue}{+5-x } & = & 1 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & 1 \color{blue}{+5} \\\Leftrightarrow &4x & = &6\\\Leftrightarrow & \color{red}{4}x & = &6\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{6}{4} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{+6}& = & 7 \color{red}{ -2x } \\\Leftrightarrow & -x \color{red}{+6}\color{blue}{-6+2x } & = & 7 \color{red}{ -2x }\color{blue}{-6+2x } \\\Leftrightarrow & -x \color{blue}{+2x } & = & 7 \color{blue}{-6} \\\Leftrightarrow &x & = &1\\\Leftrightarrow & \color{red}{}x & = &1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 1 \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{-15}& = & 7 \color{red}{ +7x } \\\Leftrightarrow & 9x \color{red}{-15}\color{blue}{+15-7x } & = & 7 \color{red}{ +7x }\color{blue}{+15-7x } \\\Leftrightarrow & 9x \color{blue}{-7x } & = & 7 \color{blue}{+15} \\\Leftrightarrow &2x & = &22\\\Leftrightarrow & \color{red}{2}x & = &22\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{22}{2} \\\Leftrightarrow & \color{green}{ x = 11 } & & \\ & V = \left\{ 11 \right\} & \\\end{align}\)