Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{-13}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-13}\color{blue}{+13-x } & = & -12 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -12 \color{blue}{+13} \\\Leftrightarrow &-14x & = &1\\\Leftrightarrow & \color{red}{-14}x & = &1\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{1}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{14} } & & \\ & V = \left\{ \frac{-1}{14} \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{-5}& = & -15 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{-5}\color{blue}{+5+4x } & = & -15 \color{red}{ -4x }\color{blue}{+5+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -15 \color{blue}{+5} \\\Leftrightarrow &13x & = &-10\\\Leftrightarrow & \color{red}{13}x & = &-10\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-10}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{13} } & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{-10}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-10}\color{blue}{+10-x } & = & -7 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -7 \color{blue}{+10} \\\Leftrightarrow &-15x & = &3\\\Leftrightarrow & \color{red}{-15}x & = &3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{+12}& = & -10 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{+12}\color{blue}{-12-9x } & = & -10 \color{red}{ +9x }\color{blue}{-12-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & -10 \color{blue}{-12} \\\Leftrightarrow &-13x & = &-22\\\Leftrightarrow & \color{red}{-13}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-22}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{22}{13} } & & \\ & V = \left\{ \frac{22}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{+6}& = & 7 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{+6}\color{blue}{-6-9x } & = & 7 \color{red}{ +9x }\color{blue}{-6-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & 7 \color{blue}{-6} \\\Leftrightarrow &-13x & = &1\\\Leftrightarrow & \color{red}{-13}x & = &1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{+7}& = & -12 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+7}\color{blue}{-7+6x } & = & -12 \color{red}{ -6x }\color{blue}{-7+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -12 \color{blue}{-7} \\\Leftrightarrow &19x & = &-19\\\Leftrightarrow & \color{red}{19}x & = &-19\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-19}{19} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{-10}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-10}\color{blue}{+10-x } & = & -9 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & -9 \color{blue}{+10} \\\Leftrightarrow &3x & = &1\\\Leftrightarrow & \color{red}{3}x & = &1\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{1}{3} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{-15}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-15}\color{blue}{+15-x } & = & 12 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 12 \color{blue}{+15} \\\Leftrightarrow &-3x & = &27\\\Leftrightarrow & \color{red}{-3}x & = &27\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{27}{-3} \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{-8}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-8}\color{blue}{+8-x } & = & -2 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -2 \color{blue}{+8} \\\Leftrightarrow &-5x & = &6\\\Leftrightarrow & \color{red}{-5}x & = &6\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{6}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{+15}& = & 8 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{+15}\color{blue}{-15+7x } & = & 8 \color{red}{ -7x }\color{blue}{-15+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & 8 \color{blue}{-15} \\\Leftrightarrow &19x & = &-7\\\Leftrightarrow & \color{red}{19}x & = &-7\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-7}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{19} } & & \\ & V = \left\{ \frac{-7}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{-9}& = & 12 \color{red}{ -13x } \\\Leftrightarrow & x \color{red}{-9}\color{blue}{+9+13x } & = & 12 \color{red}{ -13x }\color{blue}{+9+13x } \\\Leftrightarrow & x \color{blue}{+13x } & = & 12 \color{blue}{+9} \\\Leftrightarrow &14x & = &21\\\Leftrightarrow & \color{red}{14}x & = &21\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{21}{14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{+9}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+9}\color{blue}{-9-x } & = & 9 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 9 \color{blue}{-9} \\\Leftrightarrow &-14x & = &0\\\Leftrightarrow & \color{red}{-14}x & = &0\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{0}{-14} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)