Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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