Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{-8}& = & -8 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8+13x } & = & -8 \color{red}{ -13x }\color{blue}{+8+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -8 \color{blue}{+8} \\\Leftrightarrow &27x & = &0\\\Leftrightarrow & \color{red}{27}x & = &0\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{0}{27} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{+7}& = & 3 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{+7}\color{blue}{-7+11x } & = & 3 \color{red}{ -11x }\color{blue}{-7+11x } \\\Leftrightarrow & 9x \color{blue}{+11x } & = & 3 \color{blue}{-7} \\\Leftrightarrow &20x & = &-4\\\Leftrightarrow & \color{red}{20}x & = &-4\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-4}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{+13}& = & 5 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+13}\color{blue}{-13-x } & = & 5 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 5 \color{blue}{-13} \\\Leftrightarrow &11x & = &-8\\\Leftrightarrow & \color{red}{11}x & = &-8\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-8}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{11} } & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{-14}& = & 6 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{-14}\color{blue}{+14+12x } & = & 6 \color{red}{ -12x }\color{blue}{+14+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & 6 \color{blue}{+14} \\\Leftrightarrow &25x & = &20\\\Leftrightarrow & \color{red}{25}x & = &20\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{20}{25} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{-1}& = & 11 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{-1}\color{blue}{+1-11x } & = & 11 \color{red}{ +11x }\color{blue}{+1-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & 11 \color{blue}{+1} \\\Leftrightarrow &-5x & = &12\\\Leftrightarrow & \color{red}{-5}x & = &12\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{12}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{5} } & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{-8}& = & -9 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{-8}\color{blue}{+8+3x } & = & -9 \color{red}{ -3x }\color{blue}{+8+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & -9 \color{blue}{+8} \\\Leftrightarrow &10x & = &-1\\\Leftrightarrow & \color{red}{10}x & = &-1\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-1}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{-8}& = & 2 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8-9x } & = & 2 \color{red}{ +9x }\color{blue}{+8-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & 2 \color{blue}{+8} \\\Leftrightarrow &5x & = &10\\\Leftrightarrow & \color{red}{5}x & = &10\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{10}{5} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{-5}& = & -9 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{-5}\color{blue}{+5-11x } & = & -9 \color{red}{ +11x }\color{blue}{+5-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & -9 \color{blue}{+5} \\\Leftrightarrow &-16x & = &-4\\\Leftrightarrow & \color{red}{-16}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-4}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{+4}& = & -15 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{+4}\color{blue}{-4-11x } & = & -15 \color{red}{ +11x }\color{blue}{-4-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & -15 \color{blue}{-4} \\\Leftrightarrow &4x & = &-19\\\Leftrightarrow & \color{red}{4}x & = &-19\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-19}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{4} } & & \\ & V = \left\{ \frac{-19}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{-3}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-3}\color{blue}{+3-x } & = & 3 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 3 \color{blue}{+3} \\\Leftrightarrow &-8x & = &6\\\Leftrightarrow & \color{red}{-8}x & = &6\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{6}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{-7}& = & 3 \color{red}{ +8x } \\\Leftrightarrow & 7x \color{red}{-7}\color{blue}{+7-8x } & = & 3 \color{red}{ +8x }\color{blue}{+7-8x } \\\Leftrightarrow & 7x \color{blue}{-8x } & = & 3 \color{blue}{+7} \\\Leftrightarrow &-x & = &10\\\Leftrightarrow & \color{red}{-}x & = &10\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{10}{-1} \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{-2}& = & 11 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{-2}\color{blue}{+2-9x } & = & 11 \color{red}{ +9x }\color{blue}{+2-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & 11 \color{blue}{+2} \\\Leftrightarrow &-20x & = &13\\\Leftrightarrow & \color{red}{-20}x & = &13\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{13}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{20} } & & \\ & V = \left\{ \frac{-13}{20} \right\} & \\\end{align}\)