Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{+11}& = & 4 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+11}\color{blue}{-11+7x } & = & 4 \color{red}{ -7x }\color{blue}{-11+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & 4 \color{blue}{-11} \\\Leftrightarrow &11x & = &-7\\\Leftrightarrow & \color{red}{11}x & = &-7\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-7}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{+11}& = & 12 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+11}\color{blue}{-11-7x } & = & 12 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 12 \color{blue}{-11} \\\Leftrightarrow &-20x & = &1\\\Leftrightarrow & \color{red}{-20}x & = &1\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{1}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{20} } & & \\ & V = \left\{ \frac{-1}{20} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{+10}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+10}\color{blue}{-10-x } & = & -12 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -12 \color{blue}{-10} \\\Leftrightarrow &13x & = &-22\\\Leftrightarrow & \color{red}{13}x & = &-22\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-22}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{13} } & & \\ & V = \left\{ \frac{-22}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{+8}& = & 9 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+8}\color{blue}{-8+7x } & = & 9 \color{red}{ -7x }\color{blue}{-8+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & 9 \color{blue}{-8} \\\Leftrightarrow &11x & = &1\\\Leftrightarrow & \color{red}{11}x & = &1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{-3}& = & 11 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{-3}\color{blue}{+3-x } & = & 11 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & 11 \color{blue}{+3} \\\Leftrightarrow &12x & = &14\\\Leftrightarrow & \color{red}{12}x & = &14\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{14}{12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{6} } & & \\ & V = \left\{ \frac{7}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{+5}& = & -13 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{+5}\color{blue}{-5-5x } & = & -13 \color{red}{ +5x }\color{blue}{-5-5x } \\\Leftrightarrow & -2x \color{blue}{-5x } & = & -13 \color{blue}{-5} \\\Leftrightarrow &-7x & = &-18\\\Leftrightarrow & \color{red}{-7}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-18}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{18}{7} } & & \\ & V = \left\{ \frac{18}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{-6}& = & -4 \color{red}{ -2x } \\\Leftrightarrow & 9x \color{red}{-6}\color{blue}{+6+2x } & = & -4 \color{red}{ -2x }\color{blue}{+6+2x } \\\Leftrightarrow & 9x \color{blue}{+2x } & = & -4 \color{blue}{+6} \\\Leftrightarrow &11x & = &2\\\Leftrightarrow & \color{red}{11}x & = &2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{-9}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-9}\color{blue}{+9-7x } & = & 11 \color{red}{ +7x }\color{blue}{+9-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 11 \color{blue}{+9} \\\Leftrightarrow &-17x & = &20\\\Leftrightarrow & \color{red}{-17}x & = &20\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{20}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{17} } & & \\ & V = \left\{ \frac{-20}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{+2}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+2}\color{blue}{-2-x } & = & 2 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 2 \color{blue}{-2} \\\Leftrightarrow &-12x & = &0\\\Leftrightarrow & \color{red}{-12}x & = &0\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{0}{-12} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{-13}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-13}\color{blue}{+13-x } & = & 10 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 10 \color{blue}{+13} \\\Leftrightarrow &-5x & = &23\\\Leftrightarrow & \color{red}{-5}x & = &23\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{23}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{5} } & & \\ & V = \left\{ \frac{-23}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{+8}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+8}\color{blue}{-8-x } & = & 7 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 7 \color{blue}{-8} \\\Leftrightarrow &7x & = &-1\\\Leftrightarrow & \color{red}{7}x & = &-1\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-1}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{+7}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+7}\color{blue}{-7-x } & = & 10 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 10 \color{blue}{-7} \\\Leftrightarrow &-5x & = &3\\\Leftrightarrow & \color{red}{-5}x & = &3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)