Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{-5}& = & -5 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{-5}\color{blue}{+5+2x } & = & -5 \color{red}{ -2x }\color{blue}{+5+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & -5 \color{blue}{+5} \\\Leftrightarrow &5x & = &0\\\Leftrightarrow & \color{red}{5}x & = &0\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{0}{5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-1}& = & 3 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-1}\color{blue}{+1+11x } & = & 3 \color{red}{ -11x }\color{blue}{+1+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 3 \color{blue}{+1} \\\Leftrightarrow &23x & = &4\\\Leftrightarrow & \color{red}{23}x & = &4\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{4}{23} \\\Leftrightarrow & \color{green}{ x = \frac{4}{23} } & & \\ & V = \left\{ \frac{4}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{+5}& = & 8 \color{red}{ +7x } \\\Leftrightarrow & -2x \color{red}{+5}\color{blue}{-5-7x } & = & 8 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & -2x \color{blue}{-7x } & = & 8 \color{blue}{-5} \\\Leftrightarrow &-9x & = &3\\\Leftrightarrow & \color{red}{-9}x & = &3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{-6}& = & 6 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{-6}\color{blue}{+6+8x } & = & 6 \color{red}{ -8x }\color{blue}{+6+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & 6 \color{blue}{+6} \\\Leftrightarrow &17x & = &12\\\Leftrightarrow & \color{red}{17}x & = &12\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{12}{17} \\\Leftrightarrow & \color{green}{ x = \frac{12}{17} } & & \\ & V = \left\{ \frac{12}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+9}& = & -15 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+9}\color{blue}{-9-9x } & = & -15 \color{red}{ +9x }\color{blue}{-9-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -15 \color{blue}{-9} \\\Leftrightarrow &-17x & = &-24\\\Leftrightarrow & \color{red}{-17}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-24}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{24}{17} } & & \\ & V = \left\{ \frac{24}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{-1}& = & 15 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{-1}\color{blue}{+1+12x } & = & 15 \color{red}{ -12x }\color{blue}{+1+12x } \\\Leftrightarrow & 5x \color{blue}{+12x } & = & 15 \color{blue}{+1} \\\Leftrightarrow &17x & = &16\\\Leftrightarrow & \color{red}{17}x & = &16\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{16}{17} \\\Leftrightarrow & \color{green}{ x = \frac{16}{17} } & & \\ & V = \left\{ \frac{16}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{-7}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-7}\color{blue}{+7-x } & = & 5 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 5 \color{blue}{+7} \\\Leftrightarrow &-11x & = &12\\\Leftrightarrow & \color{red}{-11}x & = &12\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{12}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{11} } & & \\ & V = \left\{ \frac{-12}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{-1}& = & 12 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{-1}\color{blue}{+1+7x } & = & 12 \color{red}{ -7x }\color{blue}{+1+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & 12 \color{blue}{+1} \\\Leftrightarrow &19x & = &13\\\Leftrightarrow & \color{red}{19}x & = &13\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{13}{19} \\\Leftrightarrow & \color{green}{ x = \frac{13}{19} } & & \\ & V = \left\{ \frac{13}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{-7}& = & -8 \color{red}{ +12x } \\\Leftrightarrow & -x \color{red}{-7}\color{blue}{+7-12x } & = & -8 \color{red}{ +12x }\color{blue}{+7-12x } \\\Leftrightarrow & -x \color{blue}{-12x } & = & -8 \color{blue}{+7} \\\Leftrightarrow &-13x & = &-1\\\Leftrightarrow & \color{red}{-13}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{-1}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-1}\color{blue}{+1-x } & = & -3 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -3 \color{blue}{+1} \\\Leftrightarrow &11x & = &-2\\\Leftrightarrow & \color{red}{11}x & = &-2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{+5}& = & -15 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+5}\color{blue}{-5-14x } & = & -15 \color{red}{ +14x }\color{blue}{-5-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -15 \color{blue}{-5} \\\Leftrightarrow &-23x & = &-20\\\Leftrightarrow & \color{red}{-23}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-20}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{20}{23} } & & \\ & V = \left\{ \frac{20}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{-13}& = & -5 \color{red}{ +4x } \\\Leftrightarrow & -x \color{red}{-13}\color{blue}{+13-4x } & = & -5 \color{red}{ +4x }\color{blue}{+13-4x } \\\Leftrightarrow & -x \color{blue}{-4x } & = & -5 \color{blue}{+13} \\\Leftrightarrow &-5x & = &8\\\Leftrightarrow & \color{red}{-5}x & = &8\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{8}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)