Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{-11}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11-x } & = & 3 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 3 \color{blue}{+11} \\\Leftrightarrow &-6x & = &14\\\Leftrightarrow & \color{red}{-6}x & = &14\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{14}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{+14}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & -2x \color{red}{+14}\color{blue}{-14-13x } & = & -7 \color{red}{ +13x }\color{blue}{-14-13x } \\\Leftrightarrow & -2x \color{blue}{-13x } & = & -7 \color{blue}{-14} \\\Leftrightarrow &-15x & = &-21\\\Leftrightarrow & \color{red}{-15}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-21}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{-8}& = & 14 \color{red}{ +11x } \\\Leftrightarrow & 4x \color{red}{-8}\color{blue}{+8-11x } & = & 14 \color{red}{ +11x }\color{blue}{+8-11x } \\\Leftrightarrow & 4x \color{blue}{-11x } & = & 14 \color{blue}{+8} \\\Leftrightarrow &-7x & = &22\\\Leftrightarrow & \color{red}{-7}x & = &22\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{22}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{7} } & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{+10}& = & -1 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{+10}\color{blue}{-10-9x } & = & -1 \color{red}{ +9x }\color{blue}{-10-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & -1 \color{blue}{-10} \\\Leftrightarrow &5x & = &-11\\\Leftrightarrow & \color{red}{5}x & = &-11\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-11}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{5} } & & \\ & V = \left\{ \frac{-11}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{+10}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+10}\color{blue}{-10-x } & = & -13 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -13 \color{blue}{-10} \\\Leftrightarrow &-4x & = &-23\\\Leftrightarrow & \color{red}{-4}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-23}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{23}{4} } & & \\ & V = \left\{ \frac{23}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{-6}& = & 10 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{-6}\color{blue}{+6-7x } & = & 10 \color{red}{ +7x }\color{blue}{+6-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & 10 \color{blue}{+6} \\\Leftrightarrow &-5x & = &16\\\Leftrightarrow & \color{red}{-5}x & = &16\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{16}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{5} } & & \\ & V = \left\{ \frac{-16}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{-6}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-6}\color{blue}{+6-x } & = & -6 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -6 \color{blue}{+6} \\\Leftrightarrow &-4x & = &0\\\Leftrightarrow & \color{red}{-4}x & = &0\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{0}{-4} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{-12}& = & 10 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{-12}\color{blue}{+12+5x } & = & 10 \color{red}{ -5x }\color{blue}{+12+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & 10 \color{blue}{+12} \\\Leftrightarrow &16x & = &22\\\Leftrightarrow & \color{red}{16}x & = &22\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{22}{16} \\\Leftrightarrow & \color{green}{ x = \frac{11}{8} } & & \\ & V = \left\{ \frac{11}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{-13}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-13}\color{blue}{+13-x } & = & -14 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & -14 \color{blue}{+13} \\\Leftrightarrow &9x & = &-1\\\Leftrightarrow & \color{red}{9}x & = &-1\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-1}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{9} } & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{-12}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-12}\color{blue}{+12-x } & = & -6 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -6 \color{blue}{+12} \\\Leftrightarrow &-8x & = &6\\\Leftrightarrow & \color{red}{-8}x & = &6\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{6}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{+8}& = & 13 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{+8}\color{blue}{-8+3x } & = & 13 \color{red}{ -3x }\color{blue}{-8+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & 13 \color{blue}{-8} \\\Leftrightarrow &10x & = &5\\\Leftrightarrow & \color{red}{10}x & = &5\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{5}{10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{-6}& = & -9 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{-6}\color{blue}{+6-8x } & = & -9 \color{red}{ +8x }\color{blue}{+6-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & -9 \color{blue}{+6} \\\Leftrightarrow &-15x & = &-3\\\Leftrightarrow & \color{red}{-15}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)