Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{+13}& = & -10 \color{red}{ +3x } \\\Leftrightarrow & 8x \color{red}{+13}\color{blue}{-13-3x } & = & -10 \color{red}{ +3x }\color{blue}{-13-3x } \\\Leftrightarrow & 8x \color{blue}{-3x } & = & -10 \color{blue}{-13} \\\Leftrightarrow &5x & = &-23\\\Leftrightarrow & \color{red}{5}x & = &-23\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-23}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{5} } & & \\ & V = \left\{ \frac{-23}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{-5}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-5}\color{blue}{+5-x } & = & -8 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -8 \color{blue}{+5} \\\Leftrightarrow &-7x & = &-3\\\Leftrightarrow & \color{red}{-7}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{-4}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-4}\color{blue}{+4-x } & = & -2 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -2 \color{blue}{+4} \\\Leftrightarrow &-12x & = &2\\\Leftrightarrow & \color{red}{-12}x & = &2\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{2}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{+6}& = & -1 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{+6}\color{blue}{-6-11x } & = & -1 \color{red}{ +11x }\color{blue}{-6-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & -1 \color{blue}{-6} \\\Leftrightarrow &-16x & = &-7\\\Leftrightarrow & \color{red}{-16}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-7}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{7}{16} } & & \\ & V = \left\{ \frac{7}{16} \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{-6}& = & 13 \color{red}{ +14x } \\\Leftrightarrow & 15x \color{red}{-6}\color{blue}{+6-14x } & = & 13 \color{red}{ +14x }\color{blue}{+6-14x } \\\Leftrightarrow & 15x \color{blue}{-14x } & = & 13 \color{blue}{+6} \\\Leftrightarrow &x & = &19\\\Leftrightarrow & \color{red}{}x & = &19\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 19 \\\Leftrightarrow & \color{green}{ x = 19 } & & \\ & V = \left\{ 19 \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{+3}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+3}\color{blue}{-3-x } & = & 9 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 9 \color{blue}{-3} \\\Leftrightarrow &-14x & = &6\\\Leftrightarrow & \color{red}{-14}x & = &6\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{6}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{+11}& = & 8 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{+11}\color{blue}{-11-14x } & = & 8 \color{red}{ +14x }\color{blue}{-11-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & 8 \color{blue}{-11} \\\Leftrightarrow &-27x & = &-3\\\Leftrightarrow & \color{red}{-27}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{-3}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{-1}& = & -13 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{-1}\color{blue}{+1-13x } & = & -13 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & 12x \color{blue}{-13x } & = & -13 \color{blue}{+1} \\\Leftrightarrow &-x & = &-12\\\Leftrightarrow & \color{red}{-}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-12}{-1} \\\Leftrightarrow & \color{green}{ x = 12 } & & \\ & V = \left\{ 12 \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{+12}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+12}\color{blue}{-12-13x } & = & -10 \color{red}{ +13x }\color{blue}{-12-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -10 \color{blue}{-12} \\\Leftrightarrow &-25x & = &-22\\\Leftrightarrow & \color{red}{-25}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-22}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{22}{25} } & & \\ & V = \left\{ \frac{22}{25} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{-3}& = & -1 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{-3}\color{blue}{+3-14x } & = & -1 \color{red}{ +14x }\color{blue}{+3-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & -1 \color{blue}{+3} \\\Leftrightarrow &-25x & = &2\\\Leftrightarrow & \color{red}{-25}x & = &2\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{2}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{25} } & & \\ & V = \left\{ \frac{-2}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{-14}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & 3x \color{red}{-14}\color{blue}{+14-13x } & = & 11 \color{red}{ +13x }\color{blue}{+14-13x } \\\Leftrightarrow & 3x \color{blue}{-13x } & = & 11 \color{blue}{+14} \\\Leftrightarrow &-10x & = &25\\\Leftrightarrow & \color{red}{-10}x & = &25\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{25}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{-12}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-12}\color{blue}{+12-x } & = & 7 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 7 \color{blue}{+12} \\\Leftrightarrow &-9x & = &19\\\Leftrightarrow & \color{red}{-9}x & = &19\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{19}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{9} } & & \\ & V = \left\{ \frac{-19}{9} \right\} & \\\end{align}\)