Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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