Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{+10}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+10}\color{blue}{-10-x } & = & -6 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -6 \color{blue}{-10} \\\Leftrightarrow &-14x & = &-16\\\Leftrightarrow & \color{red}{-14}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-16}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{8}{7} } & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{+1}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+1}\color{blue}{-1-x } & = & -6 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -6 \color{blue}{-1} \\\Leftrightarrow &-6x & = &-7\\\Leftrightarrow & \color{red}{-6}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-7}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{6} } & & \\ & V = \left\{ \frac{7}{6} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{+3}& = & -3 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+3}\color{blue}{-3+13x } & = & -3 \color{red}{ -13x }\color{blue}{-3+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & -3 \color{blue}{-3} \\\Leftrightarrow &20x & = &-6\\\Leftrightarrow & \color{red}{20}x & = &-6\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-6}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{10} } & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{-9}& = & 10 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{-9}\color{blue}{+9-5x } & = & 10 \color{red}{ +5x }\color{blue}{+9-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & 10 \color{blue}{+9} \\\Leftrightarrow &-17x & = &19\\\Leftrightarrow & \color{red}{-17}x & = &19\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{19}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{17} } & & \\ & V = \left\{ \frac{-19}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{-7}& = & -15 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-7}\color{blue}{+7+13x } & = & -15 \color{red}{ -13x }\color{blue}{+7+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -15 \color{blue}{+7} \\\Leftrightarrow &23x & = &-8\\\Leftrightarrow & \color{red}{23}x & = &-8\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-8}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{23} } & & \\ & V = \left\{ \frac{-8}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{-13}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-13}\color{blue}{+13-x } & = & 11 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 11 \color{blue}{+13} \\\Leftrightarrow &-10x & = &24\\\Leftrightarrow & \color{red}{-10}x & = &24\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{24}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{5} } & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{-3}& = & 15 \color{red}{ +14x } \\\Leftrightarrow & -x \color{red}{-3}\color{blue}{+3-14x } & = & 15 \color{red}{ +14x }\color{blue}{+3-14x } \\\Leftrightarrow & -x \color{blue}{-14x } & = & 15 \color{blue}{+3} \\\Leftrightarrow &-15x & = &18\\\Leftrightarrow & \color{red}{-15}x & = &18\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{18}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{-2}& = & -8 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-2}\color{blue}{+2-9x } & = & -8 \color{red}{ +9x }\color{blue}{+2-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -8 \color{blue}{+2} \\\Leftrightarrow &-17x & = &-6\\\Leftrightarrow & \color{red}{-17}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-6}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{6}{17} } & & \\ & V = \left\{ \frac{6}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{+11}& = & 12 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+11}\color{blue}{-11+6x } & = & 12 \color{red}{ -6x }\color{blue}{-11+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 12 \color{blue}{-11} \\\Leftrightarrow &19x & = &1\\\Leftrightarrow & \color{red}{19}x & = &1\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{1}{19} \\\Leftrightarrow & \color{green}{ x = \frac{1}{19} } & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{-10}& = & -12 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{-10}\color{blue}{+10+15x } & = & -12 \color{red}{ -15x }\color{blue}{+10+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & -12 \color{blue}{+10} \\\Leftrightarrow &23x & = &-2\\\Leftrightarrow & \color{red}{23}x & = &-2\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-2}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{23} } & & \\ & V = \left\{ \frac{-2}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{+12}& = & 2 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+12}\color{blue}{-12+13x } & = & 2 \color{red}{ -13x }\color{blue}{-12+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & 2 \color{blue}{-12} \\\Leftrightarrow &20x & = &-10\\\Leftrightarrow & \color{red}{20}x & = &-10\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-10}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 3x \color{red}{+1}& = & -2 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{+1}\color{blue}{-1+2x } & = & -2 \color{red}{ -2x }\color{blue}{-1+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & -2 \color{blue}{-1} \\\Leftrightarrow &5x & = &-3\\\Leftrightarrow & \color{red}{5}x & = &-3\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-3}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)