Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{-14}& = & -15 \color{red}{ +3x } \\\Leftrightarrow & 14x \color{red}{-14}\color{blue}{+14-3x } & = & -15 \color{red}{ +3x }\color{blue}{+14-3x } \\\Leftrightarrow & 14x \color{blue}{-3x } & = & -15 \color{blue}{+14} \\\Leftrightarrow &11x & = &-1\\\Leftrightarrow & \color{red}{11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{+12}& = & -2 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{+12}\color{blue}{-12+4x } & = & -2 \color{red}{ -4x }\color{blue}{-12+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & -2 \color{blue}{-12} \\\Leftrightarrow &9x & = &-14\\\Leftrightarrow & \color{red}{9}x & = &-14\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-14}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{9} } & & \\ & V = \left\{ \frac{-14}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{+14}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 15x \color{red}{+14}\color{blue}{-14-x } & = & -10 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 15x \color{blue}{-x } & = & -10 \color{blue}{-14} \\\Leftrightarrow &14x & = &-24\\\Leftrightarrow & \color{red}{14}x & = &-24\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-24}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{7} } & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{+12}& = & 6 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{+12}\color{blue}{-12-5x } & = & 6 \color{red}{ +5x }\color{blue}{-12-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & 6 \color{blue}{-12} \\\Leftrightarrow &x & = &-6\\\Leftrightarrow & \color{red}{}x & = &-6\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -6 \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{+8}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+8}\color{blue}{-8-x } & = & 10 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 10 \color{blue}{-8} \\\Leftrightarrow &-13x & = &2\\\Leftrightarrow & \color{red}{-13}x & = &2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{13} } & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{+8}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+8}\color{blue}{-8-x } & = & -8 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -8 \color{blue}{-8} \\\Leftrightarrow &-3x & = &-16\\\Leftrightarrow & \color{red}{-3}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-16}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{16}{3} } & & \\ & V = \left\{ \frac{16}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{+2}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+2}\color{blue}{-2-x } & = & -9 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -9 \color{blue}{-2} \\\Leftrightarrow &-4x & = &-11\\\Leftrightarrow & \color{red}{-4}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-11}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{11}{4} } & & \\ & V = \left\{ \frac{11}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{+13}& = & 5 \color{red}{ +12x } \\\Leftrightarrow & -x \color{red}{+13}\color{blue}{-13-12x } & = & 5 \color{red}{ +12x }\color{blue}{-13-12x } \\\Leftrightarrow & -x \color{blue}{-12x } & = & 5 \color{blue}{-13} \\\Leftrightarrow &-13x & = &-8\\\Leftrightarrow & \color{red}{-13}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-8}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{8}{13} } & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{+13}& = & 12 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+13}\color{blue}{-13-9x } & = & 12 \color{red}{ +9x }\color{blue}{-13-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 12 \color{blue}{-13} \\\Leftrightarrow &-17x & = &-1\\\Leftrightarrow & \color{red}{-17}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-1}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{1}{17} } & & \\ & V = \left\{ \frac{1}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{-13}& = & 7 \color{red}{ +12x } \\\Leftrightarrow & -x \color{red}{-13}\color{blue}{+13-12x } & = & 7 \color{red}{ +12x }\color{blue}{+13-12x } \\\Leftrightarrow & -x \color{blue}{-12x } & = & 7 \color{blue}{+13} \\\Leftrightarrow &-13x & = &20\\\Leftrightarrow & \color{red}{-13}x & = &20\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{20}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{13} } & & \\ & V = \left\{ \frac{-20}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{+12}& = & 14 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{+12}\color{blue}{-12-14x } & = & 14 \color{red}{ +14x }\color{blue}{-12-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & 14 \color{blue}{-12} \\\Leftrightarrow &-27x & = &2\\\Leftrightarrow & \color{red}{-27}x & = &2\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{2}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{27} } & & \\ & V = \left\{ \frac{-2}{27} \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{+11}& = & 3 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+11}\color{blue}{-11+13x } & = & 3 \color{red}{ -13x }\color{blue}{-11+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & 3 \color{blue}{-11} \\\Leftrightarrow &23x & = &-8\\\Leftrightarrow & \color{red}{23}x & = &-8\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-8}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{23} } & & \\ & V = \left\{ \frac{-8}{23} \right\} & \\\end{align}\)