Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{+4}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+4}\color{blue}{-4-x } & = & -6 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -6 \color{blue}{-4} \\\Leftrightarrow &x & = &-10\\\Leftrightarrow & \color{red}{}x & = &-10\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -10 \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{+5}& = & -1 \color{red}{ +5x } \\\Leftrightarrow & -x \color{red}{+5}\color{blue}{-5-5x } & = & -1 \color{red}{ +5x }\color{blue}{-5-5x } \\\Leftrightarrow & -x \color{blue}{-5x } & = & -1 \color{blue}{-5} \\\Leftrightarrow &-6x & = &-6\\\Leftrightarrow & \color{red}{-6}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-6}{-6} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{-2}& = & 6 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-2}\color{blue}{+2-9x } & = & 6 \color{red}{ +9x }\color{blue}{+2-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 6 \color{blue}{+2} \\\Leftrightarrow &-17x & = &8\\\Leftrightarrow & \color{red}{-17}x & = &8\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{8}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{17} } & & \\ & V = \left\{ \frac{-8}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{-4}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-4}\color{blue}{+4-x } & = & -4 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -4 \color{blue}{+4} \\\Leftrightarrow &-11x & = &0\\\Leftrightarrow & \color{red}{-11}x & = &0\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{0}{-11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{+15}& = & 4 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+15}\color{blue}{-15+7x } & = & 4 \color{red}{ -7x }\color{blue}{-15+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & 4 \color{blue}{-15} \\\Leftrightarrow &11x & = &-11\\\Leftrightarrow & \color{red}{11}x & = &-11\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-11}{11} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{-7}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{-7}\color{blue}{+7-13x } & = & 3 \color{red}{ +13x }\color{blue}{+7-13x } \\\Leftrightarrow & 12x \color{blue}{-13x } & = & 3 \color{blue}{+7} \\\Leftrightarrow &-x & = &10\\\Leftrightarrow & \color{red}{-}x & = &10\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{10}{-1} \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{+5}& = & -14 \color{red}{ -2x } \\\Leftrightarrow & x \color{red}{+5}\color{blue}{-5+2x } & = & -14 \color{red}{ -2x }\color{blue}{-5+2x } \\\Leftrightarrow & x \color{blue}{+2x } & = & -14 \color{blue}{-5} \\\Leftrightarrow &3x & = &-19\\\Leftrightarrow & \color{red}{3}x & = &-19\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-19}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{3} } & & \\ & V = \left\{ \frac{-19}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{+14}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+14}\color{blue}{-14-x } & = & 14 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 14 \color{blue}{-14} \\\Leftrightarrow &-16x & = &0\\\Leftrightarrow & \color{red}{-16}x & = &0\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{0}{-16} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{-9}& = & 2 \color{red}{ +7x } \\\Leftrightarrow & -2x \color{red}{-9}\color{blue}{+9-7x } & = & 2 \color{red}{ +7x }\color{blue}{+9-7x } \\\Leftrightarrow & -2x \color{blue}{-7x } & = & 2 \color{blue}{+9} \\\Leftrightarrow &-9x & = &11\\\Leftrightarrow & \color{red}{-9}x & = &11\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{11}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{9} } & & \\ & V = \left\{ \frac{-11}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{-15}& = & 10 \color{red}{ +2x } \\\Leftrightarrow & 9x \color{red}{-15}\color{blue}{+15-2x } & = & 10 \color{red}{ +2x }\color{blue}{+15-2x } \\\Leftrightarrow & 9x \color{blue}{-2x } & = & 10 \color{blue}{+15} \\\Leftrightarrow &7x & = &25\\\Leftrightarrow & \color{red}{7}x & = &25\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{25}{7} \\\Leftrightarrow & \color{green}{ x = \frac{25}{7} } & & \\ & V = \left\{ \frac{25}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{+3}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+3}\color{blue}{-3-x } & = & 12 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 12 \color{blue}{-3} \\\Leftrightarrow &-15x & = &9\\\Leftrightarrow & \color{red}{-15}x & = &9\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{9}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{-8}& = & -5 \color{red}{ -5x } \\\Leftrightarrow & 13x \color{red}{-8}\color{blue}{+8+5x } & = & -5 \color{red}{ -5x }\color{blue}{+8+5x } \\\Leftrightarrow & 13x \color{blue}{+5x } & = & -5 \color{blue}{+8} \\\Leftrightarrow &18x & = &3\\\Leftrightarrow & \color{red}{18}x & = &3\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}} & = & \frac{3}{18} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)