Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{-2}& = & 14 \color{red}{ +5x } \\\Leftrightarrow & -x \color{red}{-2}\color{blue}{+2-5x } & = & 14 \color{red}{ +5x }\color{blue}{+2-5x } \\\Leftrightarrow & -x \color{blue}{-5x } & = & 14 \color{blue}{+2} \\\Leftrightarrow &-6x & = &16\\\Leftrightarrow & \color{red}{-6}x & = &16\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{16}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{-14}& = & -5 \color{red}{ -2x } \\\Leftrightarrow & x \color{red}{-14}\color{blue}{+14+2x } & = & -5 \color{red}{ -2x }\color{blue}{+14+2x } \\\Leftrightarrow & x \color{blue}{+2x } & = & -5 \color{blue}{+14} \\\Leftrightarrow &3x & = &9\\\Leftrightarrow & \color{red}{3}x & = &9\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{9}{3} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{-2}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-2}\color{blue}{+2-x } & = & 6 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 6 \color{blue}{+2} \\\Leftrightarrow &-8x & = &8\\\Leftrightarrow & \color{red}{-8}x & = &8\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{8}{-8} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{-12}& = & 11 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-12}\color{blue}{+12+11x } & = & 11 \color{red}{ -11x }\color{blue}{+12+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 11 \color{blue}{+12} \\\Leftrightarrow &23x & = &23\\\Leftrightarrow & \color{red}{23}x & = &23\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{23}{23} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{+2}& = & 10 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{+2}\color{blue}{-2+5x } & = & 10 \color{red}{ -5x }\color{blue}{-2+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & 10 \color{blue}{-2} \\\Leftrightarrow &8x & = &8\\\Leftrightarrow & \color{red}{8}x & = &8\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{8}{8} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{-7}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-7}\color{blue}{+7-x } & = & -12 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -12 \color{blue}{+7} \\\Leftrightarrow &-15x & = &-5\\\Leftrightarrow & \color{red}{-15}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{+1}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+1}\color{blue}{-1-x } & = & -8 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -8 \color{blue}{-1} \\\Leftrightarrow &-9x & = &-9\\\Leftrightarrow & \color{red}{-9}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-9}{-9} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{+2}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+2}\color{blue}{-2-x } & = & 15 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 15 \color{blue}{-2} \\\Leftrightarrow &-15x & = &13\\\Leftrightarrow & \color{red}{-15}x & = &13\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{13}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{15} } & & \\ & V = \left\{ \frac{-13}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{+11}& = & 9 \color{red}{ +7x } \\\Leftrightarrow & 13x \color{red}{+11}\color{blue}{-11-7x } & = & 9 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & 13x \color{blue}{-7x } & = & 9 \color{blue}{-11} \\\Leftrightarrow &6x & = &-2\\\Leftrightarrow & \color{red}{6}x & = &-2\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-2}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{+10}& = & 1 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{+10}\color{blue}{-10+5x } & = & 1 \color{red}{ -5x }\color{blue}{-10+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & 1 \color{blue}{-10} \\\Leftrightarrow &16x & = &-9\\\Leftrightarrow & \color{red}{16}x & = &-9\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-9}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{16} } & & \\ & V = \left\{ \frac{-9}{16} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{-13}& = & 10 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{-13}\color{blue}{+13-11x } & = & 10 \color{red}{ +11x }\color{blue}{+13-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & 10 \color{blue}{+13} \\\Leftrightarrow &-5x & = &23\\\Leftrightarrow & \color{red}{-5}x & = &23\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{23}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{5} } & & \\ & V = \left\{ \frac{-23}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{+14}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+14}\color{blue}{-14-x } & = & 14 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 14 \color{blue}{-14} \\\Leftrightarrow &-6x & = &0\\\Leftrightarrow & \color{red}{-6}x & = &0\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{0}{-6} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)