Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{-10}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-10}\color{blue}{+10-x } & = & -14 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -14 \color{blue}{+10} \\\Leftrightarrow &-13x & = &-4\\\Leftrightarrow & \color{red}{-13}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{+2}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{+2}\color{blue}{-2-x } & = & -4 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & -4 \color{blue}{-2} \\\Leftrightarrow &8x & = &-6\\\Leftrightarrow & \color{red}{8}x & = &-6\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-6}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{-6}& = & -6 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-6}\color{blue}{+6+11x } & = & -6 \color{red}{ -11x }\color{blue}{+6+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -6 \color{blue}{+6} \\\Leftrightarrow &23x & = &0\\\Leftrightarrow & \color{red}{23}x & = &0\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{0}{23} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{-5}& = & -10 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{-5}\color{blue}{+5+5x } & = & -10 \color{red}{ -5x }\color{blue}{+5+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & -10 \color{blue}{+5} \\\Leftrightarrow &11x & = &-5\\\Leftrightarrow & \color{red}{11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{-8}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-8}\color{blue}{+8-x } & = & -4 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -4 \color{blue}{+8} \\\Leftrightarrow &-14x & = &4\\\Leftrightarrow & \color{red}{-14}x & = &4\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{4}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{+3}& = & -13 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+3}\color{blue}{-3-5x } & = & -13 \color{red}{ +5x }\color{blue}{-3-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & -13 \color{blue}{-3} \\\Leftrightarrow &-9x & = &-16\\\Leftrightarrow & \color{red}{-9}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-16}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{16}{9} } & & \\ & V = \left\{ \frac{16}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{-12}& = & -6 \color{red}{ +9x } \\\Leftrightarrow & -2x \color{red}{-12}\color{blue}{+12-9x } & = & -6 \color{red}{ +9x }\color{blue}{+12-9x } \\\Leftrightarrow & -2x \color{blue}{-9x } & = & -6 \color{blue}{+12} \\\Leftrightarrow &-11x & = &6\\\Leftrightarrow & \color{red}{-11}x & = &6\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{6}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{+1}& = & -13 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{+1}\color{blue}{-1-11x } & = & -13 \color{red}{ +11x }\color{blue}{-1-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & -13 \color{blue}{-1} \\\Leftrightarrow &-5x & = &-14\\\Leftrightarrow & \color{red}{-5}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-14}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{14}{5} } & & \\ & V = \left\{ \frac{14}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{+3}& = & -15 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{+3}\color{blue}{-3+12x } & = & -15 \color{red}{ -12x }\color{blue}{-3+12x } \\\Leftrightarrow & 5x \color{blue}{+12x } & = & -15 \color{blue}{-3} \\\Leftrightarrow &17x & = &-18\\\Leftrightarrow & \color{red}{17}x & = &-18\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-18}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{17} } & & \\ & V = \left\{ \frac{-18}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{-10}& = & 2 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{-10}\color{blue}{+10-12x } & = & 2 \color{red}{ +12x }\color{blue}{+10-12x } \\\Leftrightarrow & 11x \color{blue}{-12x } & = & 2 \color{blue}{+10} \\\Leftrightarrow &-x & = &12\\\Leftrightarrow & \color{red}{-}x & = &12\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{12}{-1} \\\Leftrightarrow & \color{green}{ x = -12 } & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{+14}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+14}\color{blue}{-14-x } & = & -2 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -2 \color{blue}{-14} \\\Leftrightarrow &11x & = &-16\\\Leftrightarrow & \color{red}{11}x & = &-16\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-16}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{11} } & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{-1}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-1}\color{blue}{+1-x } & = & 5 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 5 \color{blue}{+1} \\\Leftrightarrow &-9x & = &6\\\Leftrightarrow & \color{red}{-9}x & = &6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)