Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{+15}& = & -1 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{+15}\color{blue}{-15+5x } & = & -1 \color{red}{ -5x }\color{blue}{-15+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & -1 \color{blue}{-15} \\\Leftrightarrow &8x & = &-16\\\Leftrightarrow & \color{red}{8}x & = &-16\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-16}{8} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{-14}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-14}\color{blue}{+14-x } & = & -3 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -3 \color{blue}{+14} \\\Leftrightarrow &-8x & = &11\\\Leftrightarrow & \color{red}{-8}x & = &11\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{11}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{8} } & & \\ & V = \left\{ \frac{-11}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{+13}& = & 10 \color{red}{ +13x } \\\Leftrightarrow & x \color{red}{+13}\color{blue}{-13-13x } & = & 10 \color{red}{ +13x }\color{blue}{-13-13x } \\\Leftrightarrow & x \color{blue}{-13x } & = & 10 \color{blue}{-13} \\\Leftrightarrow &-12x & = &-3\\\Leftrightarrow & \color{red}{-12}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-3}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{-8}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-8}\color{blue}{+8-x } & = & 11 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 11 \color{blue}{+8} \\\Leftrightarrow &-5x & = &19\\\Leftrightarrow & \color{red}{-5}x & = &19\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{19}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{5} } & & \\ & V = \left\{ \frac{-19}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{-10}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-10}\color{blue}{+10-x } & = & 2 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 2 \color{blue}{+10} \\\Leftrightarrow &-3x & = &12\\\Leftrightarrow & \color{red}{-3}x & = &12\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{12}{-3} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{-6}& = & -6 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{-6}\color{blue}{+6-11x } & = & -6 \color{red}{ +11x }\color{blue}{+6-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & -6 \color{blue}{+6} \\\Leftrightarrow &-21x & = &0\\\Leftrightarrow & \color{red}{-21}x & = &0\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{0}{-21} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{+13}& = & 15 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{+13}\color{blue}{-13-8x } & = & 15 \color{red}{ +8x }\color{blue}{-13-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & 15 \color{blue}{-13} \\\Leftrightarrow &-15x & = &2\\\Leftrightarrow & \color{red}{-15}x & = &2\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{2}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{15} } & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{-6}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-6}\color{blue}{+6-x } & = & -13 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -13 \color{blue}{+6} \\\Leftrightarrow &13x & = &-7\\\Leftrightarrow & \color{red}{13}x & = &-7\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-7}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{13} } & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{-9}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-9}\color{blue}{+9-x } & = & -12 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -12 \color{blue}{+9} \\\Leftrightarrow &-3x & = &-3\\\Leftrightarrow & \color{red}{-3}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-3}{-3} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{-9}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-9}\color{blue}{+9-x } & = & 10 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 10 \color{blue}{+9} \\\Leftrightarrow &-5x & = &19\\\Leftrightarrow & \color{red}{-5}x & = &19\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{19}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{5} } & & \\ & V = \left\{ \frac{-19}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{-7}& = & 13 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{-7}\color{blue}{+7-11x } & = & 13 \color{red}{ +11x }\color{blue}{+7-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & 13 \color{blue}{+7} \\\Leftrightarrow &-21x & = &20\\\Leftrightarrow & \color{red}{-21}x & = &20\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{20}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{21} } & & \\ & V = \left\{ \frac{-20}{21} \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{+3}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+3}\color{blue}{-3-x } & = & 14 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 14 \color{blue}{-3} \\\Leftrightarrow &-4x & = &11\\\Leftrightarrow & \color{red}{-4}x & = &11\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{11}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{4} } & & \\ & V = \left\{ \frac{-11}{4} \right\} & \\\end{align}\)