Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{-3}& = & -4 \color{red}{ -9x } \\\Leftrightarrow & 14x \color{red}{-3}\color{blue}{+3+9x } & = & -4 \color{red}{ -9x }\color{blue}{+3+9x } \\\Leftrightarrow & 14x \color{blue}{+9x } & = & -4 \color{blue}{+3} \\\Leftrightarrow &23x & = &-1\\\Leftrightarrow & \color{red}{23}x & = &-1\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-1}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{23} } & & \\ & V = \left\{ \frac{-1}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{-7}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-7}\color{blue}{+7-x } & = & -9 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -9 \color{blue}{+7} \\\Leftrightarrow &5x & = &-2\\\Leftrightarrow & \color{red}{5}x & = &-2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{-14}& = & 3 \color{red}{ +5x } \\\Leftrightarrow & 3x \color{red}{-14}\color{blue}{+14-5x } & = & 3 \color{red}{ +5x }\color{blue}{+14-5x } \\\Leftrightarrow & 3x \color{blue}{-5x } & = & 3 \color{blue}{+14} \\\Leftrightarrow &-2x & = &17\\\Leftrightarrow & \color{red}{-2}x & = &17\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{17}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{2} } & & \\ & V = \left\{ \frac{-17}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{-14}& = & 5 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-14}\color{blue}{+14-7x } & = & 5 \color{red}{ +7x }\color{blue}{+14-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & 5 \color{blue}{+14} \\\Leftrightarrow &-13x & = &19\\\Leftrightarrow & \color{red}{-13}x & = &19\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{19}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{13} } & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{+10}& = & -7 \color{red}{ +5x } \\\Leftrightarrow & -x \color{red}{+10}\color{blue}{-10-5x } & = & -7 \color{red}{ +5x }\color{blue}{-10-5x } \\\Leftrightarrow & -x \color{blue}{-5x } & = & -7 \color{blue}{-10} \\\Leftrightarrow &-6x & = &-17\\\Leftrightarrow & \color{red}{-6}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-17}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{17}{6} } & & \\ & V = \left\{ \frac{17}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{-14}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-14}\color{blue}{+14-x } & = & 5 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 5 \color{blue}{+14} \\\Leftrightarrow &-6x & = &19\\\Leftrightarrow & \color{red}{-6}x & = &19\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{19}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{6} } & & \\ & V = \left\{ \frac{-19}{6} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{+15}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+15}\color{blue}{-15-x } & = & -7 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -7 \color{blue}{-15} \\\Leftrightarrow &-11x & = &-22\\\Leftrightarrow & \color{red}{-11}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-22}{-11} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{+11}& = & -9 \color{red}{ -3x } \\\Leftrightarrow & -x \color{red}{+11}\color{blue}{-11+3x } & = & -9 \color{red}{ -3x }\color{blue}{-11+3x } \\\Leftrightarrow & -x \color{blue}{+3x } & = & -9 \color{blue}{-11} \\\Leftrightarrow &2x & = &-20\\\Leftrightarrow & \color{red}{2}x & = &-20\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-20}{2} \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{+2}& = & 14 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+2}\color{blue}{-2-7x } & = & 14 \color{red}{ +7x }\color{blue}{-2-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 14 \color{blue}{-2} \\\Leftrightarrow &-17x & = &12\\\Leftrightarrow & \color{red}{-17}x & = &12\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{12}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{17} } & & \\ & V = \left\{ \frac{-12}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{+11}& = & 15 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{+11}\color{blue}{-11+12x } & = & 15 \color{red}{ -12x }\color{blue}{-11+12x } \\\Leftrightarrow & 5x \color{blue}{+12x } & = & 15 \color{blue}{-11} \\\Leftrightarrow &17x & = &4\\\Leftrightarrow & \color{red}{17}x & = &4\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{4}{17} \\\Leftrightarrow & \color{green}{ x = \frac{4}{17} } & & \\ & V = \left\{ \frac{4}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{+6}& = & 8 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+6}\color{blue}{-6-5x } & = & 8 \color{red}{ +5x }\color{blue}{-6-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & 8 \color{blue}{-6} \\\Leftrightarrow &-9x & = &2\\\Leftrightarrow & \color{red}{-9}x & = &2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{-13}& = & -12 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{-13}\color{blue}{+13+9x } & = & -12 \color{red}{ -9x }\color{blue}{+13+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & -12 \color{blue}{+13} \\\Leftrightarrow &19x & = &1\\\Leftrightarrow & \color{red}{19}x & = &1\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{1}{19} \\\Leftrightarrow & \color{green}{ x = \frac{1}{19} } & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)