Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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