Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{+4}& = & 14 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+4}\color{blue}{-4-7x } & = & 14 \color{red}{ +7x }\color{blue}{-4-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 14 \color{blue}{-4} \\\Leftrightarrow &-17x & = &10\\\Leftrightarrow & \color{red}{-17}x & = &10\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{10}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{17} } & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{+12}& = & 11 \color{red}{ +9x } \\\Leftrightarrow & 7x \color{red}{+12}\color{blue}{-12-9x } & = & 11 \color{red}{ +9x }\color{blue}{-12-9x } \\\Leftrightarrow & 7x \color{blue}{-9x } & = & 11 \color{blue}{-12} \\\Leftrightarrow &-2x & = &-1\\\Leftrightarrow & \color{red}{-2}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-1}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{+2}& = & 3 \color{red}{ +2x } \\\Leftrightarrow & 15x \color{red}{+2}\color{blue}{-2-2x } & = & 3 \color{red}{ +2x }\color{blue}{-2-2x } \\\Leftrightarrow & 15x \color{blue}{-2x } & = & 3 \color{blue}{-2} \\\Leftrightarrow &13x & = &1\\\Leftrightarrow & \color{red}{13}x & = &1\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{1}{13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{+9}& = & 11 \color{red}{ +12x } \\\Leftrightarrow & 7x \color{red}{+9}\color{blue}{-9-12x } & = & 11 \color{red}{ +12x }\color{blue}{-9-12x } \\\Leftrightarrow & 7x \color{blue}{-12x } & = & 11 \color{blue}{-9} \\\Leftrightarrow &-5x & = &2\\\Leftrightarrow & \color{red}{-5}x & = &2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{+3}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+3}\color{blue}{-3-x } & = & -9 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -9 \color{blue}{-3} \\\Leftrightarrow &5x & = &-12\\\Leftrightarrow & \color{red}{5}x & = &-12\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-12}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{5} } & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{+3}& = & 12 \color{red}{ +5x } \\\Leftrightarrow & 7x \color{red}{+3}\color{blue}{-3-5x } & = & 12 \color{red}{ +5x }\color{blue}{-3-5x } \\\Leftrightarrow & 7x \color{blue}{-5x } & = & 12 \color{blue}{-3} \\\Leftrightarrow &2x & = &9\\\Leftrightarrow & \color{red}{2}x & = &9\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{9}{2} \\\Leftrightarrow & \color{green}{ x = \frac{9}{2} } & & \\ & V = \left\{ \frac{9}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{+3}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+3}\color{blue}{-3-x } & = & 9 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 9 \color{blue}{-3} \\\Leftrightarrow &-15x & = &6\\\Leftrightarrow & \color{red}{-15}x & = &6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{+6}& = & -15 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{+6}\color{blue}{-6-4x } & = & -15 \color{red}{ +4x }\color{blue}{-6-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & -15 \color{blue}{-6} \\\Leftrightarrow &-19x & = &-21\\\Leftrightarrow & \color{red}{-19}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-21}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{21}{19} } & & \\ & V = \left\{ \frac{21}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{+12}& = & 14 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+12}\color{blue}{-12+13x } & = & 14 \color{red}{ -13x }\color{blue}{-12+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & 14 \color{blue}{-12} \\\Leftrightarrow &23x & = &2\\\Leftrightarrow & \color{red}{23}x & = &2\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{2}{23} \\\Leftrightarrow & \color{green}{ x = \frac{2}{23} } & & \\ & V = \left\{ \frac{2}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{-6}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-6}\color{blue}{+6-x } & = & 13 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 13 \color{blue}{+6} \\\Leftrightarrow &-7x & = &19\\\Leftrightarrow & \color{red}{-7}x & = &19\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{19}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{7} } & & \\ & V = \left\{ \frac{-19}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{+10}& = & -3 \color{red}{ +5x } \\\Leftrightarrow & 13x \color{red}{+10}\color{blue}{-10-5x } & = & -3 \color{red}{ +5x }\color{blue}{-10-5x } \\\Leftrightarrow & 13x \color{blue}{-5x } & = & -3 \color{blue}{-10} \\\Leftrightarrow &8x & = &-13\\\Leftrightarrow & \color{red}{8}x & = &-13\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-13}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{8} } & & \\ & V = \left\{ \frac{-13}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{-11}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-11}\color{blue}{+11-x } & = & 13 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 13 \color{blue}{+11} \\\Leftrightarrow &-16x & = &24\\\Leftrightarrow & \color{red}{-16}x & = &24\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{24}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)