Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{+3}& = & -10 \color{red}{ -10x } \\\Leftrightarrow & x \color{red}{+3}\color{blue}{-3+10x } & = & -10 \color{red}{ -10x }\color{blue}{-3+10x } \\\Leftrightarrow & x \color{blue}{+10x } & = & -10 \color{blue}{-3} \\\Leftrightarrow &11x & = &-13\\\Leftrightarrow & \color{red}{11}x & = &-13\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-13}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{11} } & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{+11}& = & -5 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+11}\color{blue}{-11-7x } & = & -5 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -5 \color{blue}{-11} \\\Leftrightarrow &-13x & = &-16\\\Leftrightarrow & \color{red}{-13}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-16}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{16}{13} } & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{+9}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+9}\color{blue}{-9-x } & = & -14 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -14 \color{blue}{-9} \\\Leftrightarrow &-10x & = &-23\\\Leftrightarrow & \color{red}{-10}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-23}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{23}{10} } & & \\ & V = \left\{ \frac{23}{10} \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{-11}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-11}\color{blue}{+11-x } & = & -13 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -13 \color{blue}{+11} \\\Leftrightarrow &-15x & = &-2\\\Leftrightarrow & \color{red}{-15}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-2}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{15} } & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{+4}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+4}\color{blue}{-4-x } & = & -6 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -6 \color{blue}{-4} \\\Leftrightarrow &-7x & = &-10\\\Leftrightarrow & \color{red}{-7}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-10}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{10}{7} } & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{+11}& = & 9 \color{red}{ +7x } \\\Leftrightarrow & 4x \color{red}{+11}\color{blue}{-11-7x } & = & 9 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & 4x \color{blue}{-7x } & = & 9 \color{blue}{-11} \\\Leftrightarrow &-3x & = &-2\\\Leftrightarrow & \color{red}{-3}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{-8}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-8}\color{blue}{+8-x } & = & -2 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -2 \color{blue}{+8} \\\Leftrightarrow &-5x & = &6\\\Leftrightarrow & \color{red}{-5}x & = &6\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{6}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{+5}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+5}\color{blue}{-5-x } & = & 15 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 15 \color{blue}{-5} \\\Leftrightarrow &-3x & = &10\\\Leftrightarrow & \color{red}{-3}x & = &10\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{10}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{3} } & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{-4}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{-4}\color{blue}{+4-x } & = & 4 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & 4 \color{blue}{+4} \\\Leftrightarrow &12x & = &8\\\Leftrightarrow & \color{red}{12}x & = &8\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{8}{12} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{-14}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{-14}\color{blue}{+14-13x } & = & 9 \color{red}{ +13x }\color{blue}{+14-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & 9 \color{blue}{+14} \\\Leftrightarrow &-17x & = &23\\\Leftrightarrow & \color{red}{-17}x & = &23\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{23}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{17} } & & \\ & V = \left\{ \frac{-23}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{+3}& = & 3 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{+3}\color{blue}{-3+9x } & = & 3 \color{red}{ -9x }\color{blue}{-3+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & 3 \color{blue}{-3} \\\Leftrightarrow &19x & = &0\\\Leftrightarrow & \color{red}{19}x & = &0\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{0}{19} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{+14}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+14}\color{blue}{-14-x } & = & -13 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -13 \color{blue}{-14} \\\Leftrightarrow &-8x & = &-27\\\Leftrightarrow & \color{red}{-8}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-27}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{27}{8} } & & \\ & V = \left\{ \frac{27}{8} \right\} & \\\end{align}\)