Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{-12}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-12}\color{blue}{+12-x } & = & -8 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -8 \color{blue}{+12} \\\Leftrightarrow &-3x & = &4\\\Leftrightarrow & \color{red}{-3}x & = &4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{+7}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+7}\color{blue}{-7-x } & = & -6 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -6 \color{blue}{-7} \\\Leftrightarrow &13x & = &-13\\\Leftrightarrow & \color{red}{13}x & = &-13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-13}{13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{+7}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+7}\color{blue}{-7-x } & = & 2 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 2 \color{blue}{-7} \\\Leftrightarrow &-12x & = &-5\\\Leftrightarrow & \color{red}{-12}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-5}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{12} } & & \\ & V = \left\{ \frac{5}{12} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{+12}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+12}\color{blue}{-12-x } & = & 11 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 11 \color{blue}{-12} \\\Leftrightarrow &-16x & = &-1\\\Leftrightarrow & \color{red}{-16}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{16} } & & \\ & V = \left\{ \frac{1}{16} \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{+5}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+5}\color{blue}{-5-x } & = & -1 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -1 \color{blue}{-5} \\\Leftrightarrow &-7x & = &-6\\\Leftrightarrow & \color{red}{-7}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-6}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{-9}& = & 1 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-9}\color{blue}{+9+13x } & = & 1 \color{red}{ -13x }\color{blue}{+9+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 1 \color{blue}{+9} \\\Leftrightarrow &27x & = &10\\\Leftrightarrow & \color{red}{27}x & = &10\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{10}{27} \\\Leftrightarrow & \color{green}{ x = \frac{10}{27} } & & \\ & V = \left\{ \frac{10}{27} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{+5}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+5}\color{blue}{-5-x } & = & -9 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -9 \color{blue}{-5} \\\Leftrightarrow &-14x & = &-14\\\Leftrightarrow & \color{red}{-14}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-14}{-14} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{+8}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+8}\color{blue}{-8-x } & = & 11 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 11 \color{blue}{-8} \\\Leftrightarrow &-10x & = &3\\\Leftrightarrow & \color{red}{-10}x & = &3\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{3}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{10} } & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{+14}& = & 14 \color{red}{ -5x } \\\Leftrightarrow & x \color{red}{+14}\color{blue}{-14+5x } & = & 14 \color{red}{ -5x }\color{blue}{-14+5x } \\\Leftrightarrow & x \color{blue}{+5x } & = & 14 \color{blue}{-14} \\\Leftrightarrow &6x & = &0\\\Leftrightarrow & \color{red}{6}x & = &0\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{0}{6} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{-6}& = & -4 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{-6}\color{blue}{+6-7x } & = & -4 \color{red}{ +7x }\color{blue}{+6-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & -4 \color{blue}{+6} \\\Leftrightarrow &-5x & = &2\\\Leftrightarrow & \color{red}{-5}x & = &2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{+9}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+9}\color{blue}{-9-x } & = & -12 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -12 \color{blue}{-9} \\\Leftrightarrow &-16x & = &-21\\\Leftrightarrow & \color{red}{-16}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-21}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{21}{16} } & & \\ & V = \left\{ \frac{21}{16} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{+13}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+13}\color{blue}{-13-x } & = & 15 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 15 \color{blue}{-13} \\\Leftrightarrow &-10x & = &2\\\Leftrightarrow & \color{red}{-10}x & = &2\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{2}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)