Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{+11}& = & 8 \color{red}{ +8x } \\\Leftrightarrow & 13x \color{red}{+11}\color{blue}{-11-8x } & = & 8 \color{red}{ +8x }\color{blue}{-11-8x } \\\Leftrightarrow & 13x \color{blue}{-8x } & = & 8 \color{blue}{-11} \\\Leftrightarrow &5x & = &-3\\\Leftrightarrow & \color{red}{5}x & = &-3\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-3}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{+5}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+5}\color{blue}{-5-x } & = & 1 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 1 \color{blue}{-5} \\\Leftrightarrow &-15x & = &-4\\\Leftrightarrow & \color{red}{-15}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{15} } & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{-3}& = & 13 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{-3}\color{blue}{+3-4x } & = & 13 \color{red}{ +4x }\color{blue}{+3-4x } \\\Leftrightarrow & 3x \color{blue}{-4x } & = & 13 \color{blue}{+3} \\\Leftrightarrow &-x & = &16\\\Leftrightarrow & \color{red}{-}x & = &16\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{16}{-1} \\\Leftrightarrow & \color{green}{ x = -16 } & & \\ & V = \left\{ -16 \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{+5}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+5}\color{blue}{-5-x } & = & -13 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -13 \color{blue}{-5} \\\Leftrightarrow &11x & = &-18\\\Leftrightarrow & \color{red}{11}x & = &-18\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-18}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{11} } & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{+7}& = & -15 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{+7}\color{blue}{-7+5x } & = & -15 \color{red}{ -5x }\color{blue}{-7+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & -15 \color{blue}{-7} \\\Leftrightarrow &8x & = &-22\\\Leftrightarrow & \color{red}{8}x & = &-22\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-22}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{4} } & & \\ & V = \left\{ \frac{-11}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{+11}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+11}\color{blue}{-11-x } & = & -13 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -13 \color{blue}{-11} \\\Leftrightarrow &-8x & = &-24\\\Leftrightarrow & \color{red}{-8}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-24}{-8} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{-14}& = & 8 \color{red}{ +13x } \\\Leftrightarrow & 5x \color{red}{-14}\color{blue}{+14-13x } & = & 8 \color{red}{ +13x }\color{blue}{+14-13x } \\\Leftrightarrow & 5x \color{blue}{-13x } & = & 8 \color{blue}{+14} \\\Leftrightarrow &-8x & = &22\\\Leftrightarrow & \color{red}{-8}x & = &22\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{22}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{4} } & & \\ & V = \left\{ \frac{-11}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{+11}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{+11}\color{blue}{-11-13x } & = & 14 \color{red}{ +13x }\color{blue}{-11-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & 14 \color{blue}{-11} \\\Leftrightarrow &-17x & = &3\\\Leftrightarrow & \color{red}{-17}x & = &3\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{3}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{17} } & & \\ & V = \left\{ \frac{-3}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{-5}& = & 12 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{-5}\color{blue}{+5+11x } & = & 12 \color{red}{ -11x }\color{blue}{+5+11x } \\\Leftrightarrow & 9x \color{blue}{+11x } & = & 12 \color{blue}{+5} \\\Leftrightarrow &20x & = &17\\\Leftrightarrow & \color{red}{20}x & = &17\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{17}{20} \\\Leftrightarrow & \color{green}{ x = \frac{17}{20} } & & \\ & V = \left\{ \frac{17}{20} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{-12}& = & -10 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{-12}\color{blue}{+12-8x } & = & -10 \color{red}{ +8x }\color{blue}{+12-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & -10 \color{blue}{+12} \\\Leftrightarrow &-23x & = &2\\\Leftrightarrow & \color{red}{-23}x & = &2\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{2}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{23} } & & \\ & V = \left\{ \frac{-2}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{-7}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-7}\color{blue}{+7-x } & = & -7 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -7 \color{blue}{+7} \\\Leftrightarrow &-5x & = &0\\\Leftrightarrow & \color{red}{-5}x & = &0\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{0}{-5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{-5}& = & 11 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-5}\color{blue}{+5+11x } & = & 11 \color{red}{ -11x }\color{blue}{+5+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 11 \color{blue}{+5} \\\Leftrightarrow &17x & = &16\\\Leftrightarrow & \color{red}{17}x & = &16\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{16}{17} \\\Leftrightarrow & \color{green}{ x = \frac{16}{17} } & & \\ & V = \left\{ \frac{16}{17} \right\} & \\\end{align}\)