Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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