Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{-1}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-1}\color{blue}{+1-x } & = & -3 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -3 \color{blue}{+1} \\\Leftrightarrow &-9x & = &-2\\\Leftrightarrow & \color{red}{-9}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{9} } & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{-14}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-14}\color{blue}{+14-7x } & = & 11 \color{red}{ +7x }\color{blue}{+14-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & 11 \color{blue}{+14} \\\Leftrightarrow &-13x & = &25\\\Leftrightarrow & \color{red}{-13}x & = &25\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{25}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{13} } & & \\ & V = \left\{ \frac{-25}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{+10}& = & -9 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+10}\color{blue}{-10-7x } & = & -9 \color{red}{ +7x }\color{blue}{-10-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -9 \color{blue}{-10} \\\Leftrightarrow &-20x & = &-19\\\Leftrightarrow & \color{red}{-20}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-19}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{19}{20} } & & \\ & V = \left\{ \frac{19}{20} \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{-12}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-12}\color{blue}{+12-x } & = & 15 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 15 \color{blue}{+12} \\\Leftrightarrow &-3x & = &27\\\Leftrightarrow & \color{red}{-3}x & = &27\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{27}{-3} \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{+14}& = & -4 \color{red}{ -2x } \\\Leftrightarrow & 5x \color{red}{+14}\color{blue}{-14+2x } & = & -4 \color{red}{ -2x }\color{blue}{-14+2x } \\\Leftrightarrow & 5x \color{blue}{+2x } & = & -4 \color{blue}{-14} \\\Leftrightarrow &7x & = &-18\\\Leftrightarrow & \color{red}{7}x & = &-18\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-18}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{7} } & & \\ & V = \left\{ \frac{-18}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{+4}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+4}\color{blue}{-4-x } & = & 13 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 13 \color{blue}{-4} \\\Leftrightarrow &-3x & = &9\\\Leftrightarrow & \color{red}{-3}x & = &9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{9}{-3} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{+14}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+14}\color{blue}{-14-x } & = & -1 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -1 \color{blue}{-14} \\\Leftrightarrow &-9x & = &-15\\\Leftrightarrow & \color{red}{-9}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-15}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{-14}& = & -1 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-14}\color{blue}{+14-7x } & = & -1 \color{red}{ +7x }\color{blue}{+14-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & -1 \color{blue}{+14} \\\Leftrightarrow &3x & = &13\\\Leftrightarrow & \color{red}{3}x & = &13\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{13}{3} \\\Leftrightarrow & \color{green}{ x = \frac{13}{3} } & & \\ & V = \left\{ \frac{13}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{-8}& = & 1 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-8}\color{blue}{+8+11x } & = & 1 \color{red}{ -11x }\color{blue}{+8+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 1 \color{blue}{+8} \\\Leftrightarrow &23x & = &9\\\Leftrightarrow & \color{red}{23}x & = &9\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{9}{23} \\\Leftrightarrow & \color{green}{ x = \frac{9}{23} } & & \\ & V = \left\{ \frac{9}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{+2}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+2}\color{blue}{-2-x } & = & 4 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 4 \color{blue}{-2} \\\Leftrightarrow &-16x & = &2\\\Leftrightarrow & \color{red}{-16}x & = &2\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{2}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{+7}& = & -4 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{+7}\color{blue}{-7+13x } & = & -4 \color{red}{ -13x }\color{blue}{-7+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & -4 \color{blue}{-7} \\\Leftrightarrow &22x & = &-11\\\Leftrightarrow & \color{red}{22}x & = &-11\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-11}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{-9}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-9}\color{blue}{+9-x } & = & -9 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -9 \color{blue}{+9} \\\Leftrightarrow &-11x & = &0\\\Leftrightarrow & \color{red}{-11}x & = &0\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{0}{-11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)