Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 7x \color{red}{+11}& = & -7 \color{red}{ -9x } \\\Leftrightarrow & 7x \color{red}{+11}\color{blue}{-11+9x } & = & -7 \color{red}{ -9x }\color{blue}{-11+9x } \\\Leftrightarrow & 7x \color{blue}{+9x } & = & -7 \color{blue}{-11} \\\Leftrightarrow &16x & = &-18\\\Leftrightarrow & \color{red}{16}x & = &-18\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-18}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{8} } & & \\ & V = \left\{ \frac{-9}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{+4}& = & -14 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+4}\color{blue}{-4-13x } & = & -14 \color{red}{ +13x }\color{blue}{-4-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -14 \color{blue}{-4} \\\Leftrightarrow &-25x & = &-18\\\Leftrightarrow & \color{red}{-25}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-18}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{18}{25} } & & \\ & V = \left\{ \frac{18}{25} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{-2}& = & 15 \color{red}{ +3x } \\\Leftrightarrow & 7x \color{red}{-2}\color{blue}{+2-3x } & = & 15 \color{red}{ +3x }\color{blue}{+2-3x } \\\Leftrightarrow & 7x \color{blue}{-3x } & = & 15 \color{blue}{+2} \\\Leftrightarrow &4x & = &17\\\Leftrightarrow & \color{red}{4}x & = &17\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{17}{4} \\\Leftrightarrow & \color{green}{ x = \frac{17}{4} } & & \\ & V = \left\{ \frac{17}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{+5}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{+5}\color{blue}{-5-13x } & = & 14 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & 14 \color{blue}{-5} \\\Leftrightarrow &-16x & = &9\\\Leftrightarrow & \color{red}{-16}x & = &9\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{9}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{16} } & & \\ & V = \left\{ \frac{-9}{16} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{-4}& = & 12 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-4}\color{blue}{+4-9x } & = & 12 \color{red}{ +9x }\color{blue}{+4-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & 12 \color{blue}{+4} \\\Leftrightarrow &5x & = &16\\\Leftrightarrow & \color{red}{5}x & = &16\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{16}{5} \\\Leftrightarrow & \color{green}{ x = \frac{16}{5} } & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{-2}& = & 13 \color{red}{ +12x } \\\Leftrightarrow & x \color{red}{-2}\color{blue}{+2-12x } & = & 13 \color{red}{ +12x }\color{blue}{+2-12x } \\\Leftrightarrow & x \color{blue}{-12x } & = & 13 \color{blue}{+2} \\\Leftrightarrow &-11x & = &15\\\Leftrightarrow & \color{red}{-11}x & = &15\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{15}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{11} } & & \\ & V = \left\{ \frac{-15}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{+1}& = & -9 \color{red}{ +13x } \\\Leftrightarrow & -2x \color{red}{+1}\color{blue}{-1-13x } & = & -9 \color{red}{ +13x }\color{blue}{-1-13x } \\\Leftrightarrow & -2x \color{blue}{-13x } & = & -9 \color{blue}{-1} \\\Leftrightarrow &-15x & = &-10\\\Leftrightarrow & \color{red}{-15}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-10}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{-13}& = & -6 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{-13}\color{blue}{+13+5x } & = & -6 \color{red}{ -5x }\color{blue}{+13+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & -6 \color{blue}{+13} \\\Leftrightarrow &8x & = &7\\\Leftrightarrow & \color{red}{8}x & = &7\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{7}{8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{+3}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+3}\color{blue}{-3-x } & = & -12 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -12 \color{blue}{-3} \\\Leftrightarrow &5x & = &-15\\\Leftrightarrow & \color{red}{5}x & = &-15\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-15}{5} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{+11}& = & 13 \color{red}{ +11x } \\\Leftrightarrow & 3x \color{red}{+11}\color{blue}{-11-11x } & = & 13 \color{red}{ +11x }\color{blue}{-11-11x } \\\Leftrightarrow & 3x \color{blue}{-11x } & = & 13 \color{blue}{-11} \\\Leftrightarrow &-8x & = &2\\\Leftrightarrow & \color{red}{-8}x & = &2\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{2}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & 2x \color{red}{-13}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-13}\color{blue}{+13-x } & = & -1 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -1 \color{blue}{+13} \\\Leftrightarrow &x & = &12\\\Leftrightarrow & \color{red}{}x & = &12\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 12 \\\Leftrightarrow & \color{green}{ x = 12 } & & \\ & V = \left\{ 12 \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{-12}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-12}\color{blue}{+12-x } & = & 9 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 9 \color{blue}{+12} \\\Leftrightarrow &-13x & = &21\\\Leftrightarrow & \color{red}{-13}x & = &21\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{21}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{13} } & & \\ & V = \left\{ \frac{-21}{13} \right\} & \\\end{align}\)