Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{-13}& = & 14 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{-13}\color{blue}{+13+5x } & = & 14 \color{red}{ -5x }\color{blue}{+13+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & 14 \color{blue}{+13} \\\Leftrightarrow &16x & = &27\\\Leftrightarrow & \color{red}{16}x & = &27\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{27}{16} \\\Leftrightarrow & \color{green}{ x = \frac{27}{16} } & & \\ & V = \left\{ \frac{27}{16} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{+15}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{+15}\color{blue}{-15-x } & = & -3 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & -3 \color{blue}{-15} \\\Leftrightarrow &10x & = &-18\\\Leftrightarrow & \color{red}{10}x & = &-18\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-18}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{-2}& = & 7 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-2}\color{blue}{+2+13x } & = & 7 \color{red}{ -13x }\color{blue}{+2+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & 7 \color{blue}{+2} \\\Leftrightarrow &23x & = &9\\\Leftrightarrow & \color{red}{23}x & = &9\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{9}{23} \\\Leftrightarrow & \color{green}{ x = \frac{9}{23} } & & \\ & V = \left\{ \frac{9}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{+3}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{+3}\color{blue}{-3-x } & = & 8 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & 8 \color{blue}{-3} \\\Leftrightarrow &12x & = &5\\\Leftrightarrow & \color{red}{12}x & = &5\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{5}{12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{12} } & & \\ & V = \left\{ \frac{5}{12} \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{+6}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+6}\color{blue}{-6-x } & = & 10 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 10 \color{blue}{-6} \\\Leftrightarrow &-12x & = &4\\\Leftrightarrow & \color{red}{-12}x & = &4\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{4}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{+2}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+2}\color{blue}{-2-x } & = & -1 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -1 \color{blue}{-2} \\\Leftrightarrow &-11x & = &-3\\\Leftrightarrow & \color{red}{-11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{+15}& = & 9 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{+15}\color{blue}{-15-11x } & = & 9 \color{red}{ +11x }\color{blue}{-15-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & 9 \color{blue}{-15} \\\Leftrightarrow &-16x & = &-6\\\Leftrightarrow & \color{red}{-16}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-6}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{+14}& = & -15 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{+14}\color{blue}{-14-7x } & = & -15 \color{red}{ +7x }\color{blue}{-14-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & -15 \color{blue}{-14} \\\Leftrightarrow &-5x & = &-29\\\Leftrightarrow & \color{red}{-5}x & = &-29\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-29}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{29}{5} } & & \\ & V = \left\{ \frac{29}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{-9}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-9}\color{blue}{+9-x } & = & -7 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -7 \color{blue}{+9} \\\Leftrightarrow &-4x & = &2\\\Leftrightarrow & \color{red}{-4}x & = &2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{+14}& = & -6 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{+14}\color{blue}{-14-5x } & = & -6 \color{red}{ +5x }\color{blue}{-14-5x } \\\Leftrightarrow & -2x \color{blue}{-5x } & = & -6 \color{blue}{-14} \\\Leftrightarrow &-7x & = &-20\\\Leftrightarrow & \color{red}{-7}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-20}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{20}{7} } & & \\ & V = \left\{ \frac{20}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{+12}& = & 13 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{+12}\color{blue}{-12+3x } & = & 13 \color{red}{ -3x }\color{blue}{-12+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & 13 \color{blue}{-12} \\\Leftrightarrow &10x & = &1\\\Leftrightarrow & \color{red}{10}x & = &1\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{1}{10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{10} } & & \\ & V = \left\{ \frac{1}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & 3x \color{red}{-15}& = & 1 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-15}\color{blue}{+15+8x } & = & 1 \color{red}{ -8x }\color{blue}{+15+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & 1 \color{blue}{+15} \\\Leftrightarrow &11x & = &16\\\Leftrightarrow & \color{red}{11}x & = &16\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{16}{11} \\\Leftrightarrow & \color{green}{ x = \frac{16}{11} } & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)