Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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