Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{+14}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+14}\color{blue}{-14-x } & = & -12 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -12 \color{blue}{-14} \\\Leftrightarrow &-10x & = &-26\\\Leftrightarrow & \color{red}{-10}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-26}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{13}{5} } & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{+5}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+5}\color{blue}{-5-x } & = & 12 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 12 \color{blue}{-5} \\\Leftrightarrow &-8x & = &7\\\Leftrightarrow & \color{red}{-8}x & = &7\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{7}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{8} } & & \\ & V = \left\{ \frac{-7}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{+3}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{+3}\color{blue}{-3-x } & = & 3 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & 3 \color{blue}{-3} \\\Leftrightarrow &12x & = &0\\\Leftrightarrow & \color{red}{12}x & = &0\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{0}{12} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{-5}& = & -9 \color{red}{ +5x } \\\Leftrightarrow & 13x \color{red}{-5}\color{blue}{+5-5x } & = & -9 \color{red}{ +5x }\color{blue}{+5-5x } \\\Leftrightarrow & 13x \color{blue}{-5x } & = & -9 \color{blue}{+5} \\\Leftrightarrow &8x & = &-4\\\Leftrightarrow & \color{red}{8}x & = &-4\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-4}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{-11}& = & 15 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{-11}\color{blue}{+11-4x } & = & 15 \color{red}{ +4x }\color{blue}{+11-4x } \\\Leftrightarrow & 3x \color{blue}{-4x } & = & 15 \color{blue}{+11} \\\Leftrightarrow &-x & = &26\\\Leftrightarrow & \color{red}{-}x & = &26\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{26}{-1} \\\Leftrightarrow & \color{green}{ x = -26 } & & \\ & V = \left\{ -26 \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{-11}& = & 7 \color{red}{ +3x } \\\Leftrightarrow & -11x \color{red}{-11}\color{blue}{+11-3x } & = & 7 \color{red}{ +3x }\color{blue}{+11-3x } \\\Leftrightarrow & -11x \color{blue}{-3x } & = & 7 \color{blue}{+11} \\\Leftrightarrow &-14x & = &18\\\Leftrightarrow & \color{red}{-14}x & = &18\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{18}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{-12}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-12}\color{blue}{+12-x } & = & 5 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 5 \color{blue}{+12} \\\Leftrightarrow &-13x & = &17\\\Leftrightarrow & \color{red}{-13}x & = &17\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{17}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{13} } & & \\ & V = \left\{ \frac{-17}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{+11}& = & -14 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{+11}\color{blue}{-11-4x } & = & -14 \color{red}{ +4x }\color{blue}{-11-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & -14 \color{blue}{-11} \\\Leftrightarrow &-19x & = &-25\\\Leftrightarrow & \color{red}{-19}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-25}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{25}{19} } & & \\ & V = \left\{ \frac{25}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{-6}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-6}\color{blue}{+6-x } & = & 2 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 2 \color{blue}{+6} \\\Leftrightarrow &-4x & = &8\\\Leftrightarrow & \color{red}{-4}x & = &8\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{8}{-4} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{+14}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+14}\color{blue}{-14-x } & = & 6 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 6 \color{blue}{-14} \\\Leftrightarrow &x & = &-8\\\Leftrightarrow & \color{red}{}x & = &-8\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -8 \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{+5}& = & 15 \color{red}{ +3x } \\\Leftrightarrow & 10x \color{red}{+5}\color{blue}{-5-3x } & = & 15 \color{red}{ +3x }\color{blue}{-5-3x } \\\Leftrightarrow & 10x \color{blue}{-3x } & = & 15 \color{blue}{-5} \\\Leftrightarrow &7x & = &10\\\Leftrightarrow & \color{red}{7}x & = &10\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{10}{7} \\\Leftrightarrow & \color{green}{ x = \frac{10}{7} } & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{+1}& = & 2 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+1}\color{blue}{-1-5x } & = & 2 \color{red}{ +5x }\color{blue}{-1-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & 2 \color{blue}{-1} \\\Leftrightarrow &-9x & = &1\\\Leftrightarrow & \color{red}{-9}x & = &1\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{1}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{9} } & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)