Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{-7}& = & -7 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-7}\color{blue}{+7-9x } & = & -7 \color{red}{ +9x }\color{blue}{+7-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & -7 \color{blue}{+7} \\\Leftrightarrow &5x & = &0\\\Leftrightarrow & \color{red}{5}x & = &0\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{0}{5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{+4}& = & -14 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+4}\color{blue}{-4-9x } & = & -14 \color{red}{ +9x }\color{blue}{-4-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -14 \color{blue}{-4} \\\Leftrightarrow &-17x & = &-18\\\Leftrightarrow & \color{red}{-17}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-18}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{18}{17} } & & \\ & V = \left\{ \frac{18}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{+2}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+2}\color{blue}{-2-x } & = & 3 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 3 \color{blue}{-2} \\\Leftrightarrow &-13x & = &1\\\Leftrightarrow & \color{red}{-13}x & = &1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{-13}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-13}\color{blue}{+13-x } & = & 13 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 13 \color{blue}{+13} \\\Leftrightarrow &-6x & = &26\\\Leftrightarrow & \color{red}{-6}x & = &26\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{26}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{3} } & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{+2}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+2}\color{blue}{-2-x } & = & -10 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -10 \color{blue}{-2} \\\Leftrightarrow &-5x & = &-12\\\Leftrightarrow & \color{red}{-5}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-12}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{-2}& = & -5 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{-2}\color{blue}{+2-11x } & = & -5 \color{red}{ +11x }\color{blue}{+2-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & -5 \color{blue}{+2} \\\Leftrightarrow &x & = &-3\\\Leftrightarrow & \color{red}{}x & = &-3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -3 \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{+15}& = & 1 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{+15}\color{blue}{-15-7x } & = & 1 \color{red}{ +7x }\color{blue}{-15-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & 1 \color{blue}{-15} \\\Leftrightarrow &-16x & = &-14\\\Leftrightarrow & \color{red}{-16}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-14}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{-11}& = & -4 \color{red}{ -11x } \\\Leftrightarrow & x \color{red}{-11}\color{blue}{+11+11x } & = & -4 \color{red}{ -11x }\color{blue}{+11+11x } \\\Leftrightarrow & x \color{blue}{+11x } & = & -4 \color{blue}{+11} \\\Leftrightarrow &12x & = &7\\\Leftrightarrow & \color{red}{12}x & = &7\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{7}{12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{12} } & & \\ & V = \left\{ \frac{7}{12} \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{+1}& = & -4 \color{red}{ -7x } \\\Leftrightarrow & 5x \color{red}{+1}\color{blue}{-1+7x } & = & -4 \color{red}{ -7x }\color{blue}{-1+7x } \\\Leftrightarrow & 5x \color{blue}{+7x } & = & -4 \color{blue}{-1} \\\Leftrightarrow &12x & = &-5\\\Leftrightarrow & \color{red}{12}x & = &-5\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-5}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{12} } & & \\ & V = \left\{ \frac{-5}{12} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{-15}& = & -3 \color{red}{ -8x } \\\Leftrightarrow & 11x \color{red}{-15}\color{blue}{+15+8x } & = & -3 \color{red}{ -8x }\color{blue}{+15+8x } \\\Leftrightarrow & 11x \color{blue}{+8x } & = & -3 \color{blue}{+15} \\\Leftrightarrow &19x & = &12\\\Leftrightarrow & \color{red}{19}x & = &12\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{12}{19} \\\Leftrightarrow & \color{green}{ x = \frac{12}{19} } & & \\ & V = \left\{ \frac{12}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{-2}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-2}\color{blue}{+2-x } & = & -3 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -3 \color{blue}{+2} \\\Leftrightarrow &-13x & = &-1\\\Leftrightarrow & \color{red}{-13}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{-6}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-6}\color{blue}{+6-x } & = & 10 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 10 \color{blue}{+6} \\\Leftrightarrow &-13x & = &16\\\Leftrightarrow & \color{red}{-13}x & = &16\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{16}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{13} } & & \\ & V = \left\{ \frac{-16}{13} \right\} & \\\end{align}\)