Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{-2}& = & 8 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-2}\color{blue}{+2-14x } & = & 8 \color{red}{ +14x }\color{blue}{+2-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & 8 \color{blue}{+2} \\\Leftrightarrow &-27x & = &10\\\Leftrightarrow & \color{red}{-27}x & = &10\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{10}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{27} } & & \\ & V = \left\{ \frac{-10}{27} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{+5}& = & -13 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+5}\color{blue}{-5-5x } & = & -13 \color{red}{ +5x }\color{blue}{-5-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -13 \color{blue}{-5} \\\Leftrightarrow &7x & = &-18\\\Leftrightarrow & \color{red}{7}x & = &-18\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-18}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{7} } & & \\ & V = \left\{ \frac{-18}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{-14}& = & 7 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{-14}\color{blue}{+14-9x } & = & 7 \color{red}{ +9x }\color{blue}{+14-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & 7 \color{blue}{+14} \\\Leftrightarrow &-x & = &21\\\Leftrightarrow & \color{red}{-}x & = &21\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{21}{-1} \\\Leftrightarrow & \color{green}{ x = -21 } & & \\ & V = \left\{ -21 \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{-13}& = & -3 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-13}\color{blue}{+13+11x } & = & -3 \color{red}{ -11x }\color{blue}{+13+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -3 \color{blue}{+13} \\\Leftrightarrow &17x & = &10\\\Leftrightarrow & \color{red}{17}x & = &10\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{10}{17} \\\Leftrightarrow & \color{green}{ x = \frac{10}{17} } & & \\ & V = \left\{ \frac{10}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{-3}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-3}\color{blue}{+3-x } & = & -12 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -12 \color{blue}{+3} \\\Leftrightarrow &-8x & = &-9\\\Leftrightarrow & \color{red}{-8}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-9}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{8} } & & \\ & V = \left\{ \frac{9}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{+8}& = & -11 \color{red}{ +9x } \\\Leftrightarrow & 10x \color{red}{+8}\color{blue}{-8-9x } & = & -11 \color{red}{ +9x }\color{blue}{-8-9x } \\\Leftrightarrow & 10x \color{blue}{-9x } & = & -11 \color{blue}{-8} \\\Leftrightarrow &x & = &-19\\\Leftrightarrow & \color{red}{}x & = &-19\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -19 \\\Leftrightarrow & \color{green}{ x = -19 } & & \\ & V = \left\{ -19 \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{+11}& = & 15 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+11}\color{blue}{-11+11x } & = & 15 \color{red}{ -11x }\color{blue}{-11+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 15 \color{blue}{-11} \\\Leftrightarrow &23x & = &4\\\Leftrightarrow & \color{red}{23}x & = &4\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{4}{23} \\\Leftrightarrow & \color{green}{ x = \frac{4}{23} } & & \\ & V = \left\{ \frac{4}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{+2}& = & -13 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{+2}\color{blue}{-2+8x } & = & -13 \color{red}{ -8x }\color{blue}{-2+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & -13 \color{blue}{-2} \\\Leftrightarrow &11x & = &-15\\\Leftrightarrow & \color{red}{11}x & = &-15\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-15}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{11} } & & \\ & V = \left\{ \frac{-15}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{+12}& = & -6 \color{red}{ +12x } \\\Leftrightarrow & -7x \color{red}{+12}\color{blue}{-12-12x } & = & -6 \color{red}{ +12x }\color{blue}{-12-12x } \\\Leftrightarrow & -7x \color{blue}{-12x } & = & -6 \color{blue}{-12} \\\Leftrightarrow &-19x & = &-18\\\Leftrightarrow & \color{red}{-19}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-18}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{18}{19} } & & \\ & V = \left\{ \frac{18}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{+6}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+6}\color{blue}{-6-x } & = & 15 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 15 \color{blue}{-6} \\\Leftrightarrow &-10x & = &9\\\Leftrightarrow & \color{red}{-10}x & = &9\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{9}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{10} } & & \\ & V = \left\{ \frac{-9}{10} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{-9}& = & -14 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9-11x } & = & -14 \color{red}{ +11x }\color{blue}{+9-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & -14 \color{blue}{+9} \\\Leftrightarrow &-16x & = &-5\\\Leftrightarrow & \color{red}{-16}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-5}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{16} } & & \\ & V = \left\{ \frac{5}{16} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{+5}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & 2x \color{red}{+5}\color{blue}{-5-13x } & = & -7 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & 2x \color{blue}{-13x } & = & -7 \color{blue}{-5} \\\Leftrightarrow &-11x & = &-12\\\Leftrightarrow & \color{red}{-11}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-12}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{12}{11} } & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)