Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{+3}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+3}\color{blue}{-3-x } & = & -15 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -15 \color{blue}{-3} \\\Leftrightarrow &-13x & = &-18\\\Leftrightarrow & \color{red}{-13}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-18}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{18}{13} } & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{+1}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+1}\color{blue}{-1-x } & = & -10 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -10 \color{blue}{-1} \\\Leftrightarrow &-15x & = &-11\\\Leftrightarrow & \color{red}{-15}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-11}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{11}{15} } & & \\ & V = \left\{ \frac{11}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{-10}& = & -1 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-10}\color{blue}{+10+2x } & = & -1 \color{red}{ -2x }\color{blue}{+10+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -1 \color{blue}{+10} \\\Leftrightarrow &17x & = &9\\\Leftrightarrow & \color{red}{17}x & = &9\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{9}{17} \\\Leftrightarrow & \color{green}{ x = \frac{9}{17} } & & \\ & V = \left\{ \frac{9}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{+14}& = & 1 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+14}\color{blue}{-14+13x } & = & 1 \color{red}{ -13x }\color{blue}{-14+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & 1 \color{blue}{-14} \\\Leftrightarrow &20x & = &-13\\\Leftrightarrow & \color{red}{20}x & = &-13\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-13}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{20} } & & \\ & V = \left\{ \frac{-13}{20} \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{+2}& = & -8 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+2}\color{blue}{-2-14x } & = & -8 \color{red}{ +14x }\color{blue}{-2-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -8 \color{blue}{-2} \\\Leftrightarrow &-23x & = &-10\\\Leftrightarrow & \color{red}{-23}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-10}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{10}{23} } & & \\ & V = \left\{ \frac{10}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{+11}& = & 6 \color{red}{ +3x } \\\Leftrightarrow & 8x \color{red}{+11}\color{blue}{-11-3x } & = & 6 \color{red}{ +3x }\color{blue}{-11-3x } \\\Leftrightarrow & 8x \color{blue}{-3x } & = & 6 \color{blue}{-11} \\\Leftrightarrow &5x & = &-5\\\Leftrightarrow & \color{red}{5}x & = &-5\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-5}{5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{+11}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+11}\color{blue}{-11-x } & = & 7 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 7 \color{blue}{-11} \\\Leftrightarrow &-9x & = &-4\\\Leftrightarrow & \color{red}{-9}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-4}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{9} } & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{-5}& = & -15 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-5}\color{blue}{+5+2x } & = & -15 \color{red}{ -2x }\color{blue}{+5+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -15 \color{blue}{+5} \\\Leftrightarrow &17x & = &-10\\\Leftrightarrow & \color{red}{17}x & = &-10\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-10}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{17} } & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{+9}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+9}\color{blue}{-9-x } & = & 9 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 9 \color{blue}{-9} \\\Leftrightarrow &-3x & = &0\\\Leftrightarrow & \color{red}{-3}x & = &0\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{0}{-3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{-6}& = & -3 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{-6}\color{blue}{+6-5x } & = & -3 \color{red}{ +5x }\color{blue}{+6-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & -3 \color{blue}{+6} \\\Leftrightarrow &-9x & = &3\\\Leftrightarrow & \color{red}{-9}x & = &3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{-6}& = & -2 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{-6}\color{blue}{+6-6x } & = & -2 \color{red}{ +6x }\color{blue}{+6-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & -2 \color{blue}{+6} \\\Leftrightarrow &-11x & = &4\\\Leftrightarrow & \color{red}{-11}x & = &4\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{4}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{-11}& = & -8 \color{red}{ +3x } \\\Leftrightarrow & -14x \color{red}{-11}\color{blue}{+11-3x } & = & -8 \color{red}{ +3x }\color{blue}{+11-3x } \\\Leftrightarrow & -14x \color{blue}{-3x } & = & -8 \color{blue}{+11} \\\Leftrightarrow &-17x & = &3\\\Leftrightarrow & \color{red}{-17}x & = &3\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{3}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{17} } & & \\ & V = \left\{ \frac{-3}{17} \right\} & \\\end{align}\)