Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{-6}& = & -13 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-6}\color{blue}{+6+8x } & = & -13 \color{red}{ -8x }\color{blue}{+6+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & -13 \color{blue}{+6} \\\Leftrightarrow &11x & = &-7\\\Leftrightarrow & \color{red}{11}x & = &-7\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-7}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{-13}& = & 15 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-13}\color{blue}{+13-9x } & = & 15 \color{red}{ +9x }\color{blue}{+13-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & 15 \color{blue}{+13} \\\Leftrightarrow &5x & = &28\\\Leftrightarrow & \color{red}{5}x & = &28\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{28}{5} \\\Leftrightarrow & \color{green}{ x = \frac{28}{5} } & & \\ & V = \left\{ \frac{28}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{+14}& = & 11 \color{red}{ +5x } \\\Leftrightarrow & 4x \color{red}{+14}\color{blue}{-14-5x } & = & 11 \color{red}{ +5x }\color{blue}{-14-5x } \\\Leftrightarrow & 4x \color{blue}{-5x } & = & 11 \color{blue}{-14} \\\Leftrightarrow &-x & = &-3\\\Leftrightarrow & \color{red}{-}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-3}{-1} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{-11}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-11}\color{blue}{+11-x } & = & 2 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 2 \color{blue}{+11} \\\Leftrightarrow &-5x & = &13\\\Leftrightarrow & \color{red}{-5}x & = &13\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{13}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{5} } & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+5}& = & 10 \color{red}{ +3x } \\\Leftrightarrow & -8x \color{red}{+5}\color{blue}{-5-3x } & = & 10 \color{red}{ +3x }\color{blue}{-5-3x } \\\Leftrightarrow & -8x \color{blue}{-3x } & = & 10 \color{blue}{-5} \\\Leftrightarrow &-11x & = &5\\\Leftrightarrow & \color{red}{-11}x & = &5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{-1}& = & -2 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-1}\color{blue}{+1-7x } & = & -2 \color{red}{ +7x }\color{blue}{+1-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -2 \color{blue}{+1} \\\Leftrightarrow &-20x & = &-1\\\Leftrightarrow & \color{red}{-20}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-1}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{1}{20} } & & \\ & V = \left\{ \frac{1}{20} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{-14}& = & -4 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-14}\color{blue}{+14+11x } & = & -4 \color{red}{ -11x }\color{blue}{+14+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -4 \color{blue}{+14} \\\Leftrightarrow &23x & = &10\\\Leftrightarrow & \color{red}{23}x & = &10\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{10}{23} \\\Leftrightarrow & \color{green}{ x = \frac{10}{23} } & & \\ & V = \left\{ \frac{10}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{+4}& = & -9 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{+4}\color{blue}{-4-11x } & = & -9 \color{red}{ +11x }\color{blue}{-4-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & -9 \color{blue}{-4} \\\Leftrightarrow &4x & = &-13\\\Leftrightarrow & \color{red}{4}x & = &-13\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-13}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{4} } & & \\ & V = \left\{ \frac{-13}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{-3}& = & 8 \color{red}{ -14x } \\\Leftrightarrow & 3x \color{red}{-3}\color{blue}{+3+14x } & = & 8 \color{red}{ -14x }\color{blue}{+3+14x } \\\Leftrightarrow & 3x \color{blue}{+14x } & = & 8 \color{blue}{+3} \\\Leftrightarrow &17x & = &11\\\Leftrightarrow & \color{red}{17}x & = &11\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{11}{17} \\\Leftrightarrow & \color{green}{ x = \frac{11}{17} } & & \\ & V = \left\{ \frac{11}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{-5}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-5}\color{blue}{+5-x } & = & -12 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & -12 \color{blue}{+5} \\\Leftrightarrow &3x & = &-7\\\Leftrightarrow & \color{red}{3}x & = &-7\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-7}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{-1}& = & -7 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{-1}\color{blue}{+1-10x } & = & -7 \color{red}{ +10x }\color{blue}{+1-10x } \\\Leftrightarrow & 9x \color{blue}{-10x } & = & -7 \color{blue}{+1} \\\Leftrightarrow &-x & = &-6\\\Leftrightarrow & \color{red}{-}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-6}{-1} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{+3}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+3}\color{blue}{-3-x } & = & -15 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -15 \color{blue}{-3} \\\Leftrightarrow &-3x & = &-18\\\Leftrightarrow & \color{red}{-3}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-18}{-3} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)