Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{-8}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-8}\color{blue}{+8-x } & = & 4 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 4 \color{blue}{+8} \\\Leftrightarrow &-4x & = &12\\\Leftrightarrow & \color{red}{-4}x & = &12\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{12}{-4} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{+6}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+6}\color{blue}{-6-7x } & = & -3 \color{red}{ +7x }\color{blue}{-6-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -3 \color{blue}{-6} \\\Leftrightarrow &-17x & = &-9\\\Leftrightarrow & \color{red}{-17}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-9}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{9}{17} } & & \\ & V = \left\{ \frac{9}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{+11}& = & 1 \color{red}{ -2x } \\\Leftrightarrow & -x \color{red}{+11}\color{blue}{-11+2x } & = & 1 \color{red}{ -2x }\color{blue}{-11+2x } \\\Leftrightarrow & -x \color{blue}{+2x } & = & 1 \color{blue}{-11} \\\Leftrightarrow &x & = &-10\\\Leftrightarrow & \color{red}{}x & = &-10\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -10 \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{-1}& = & -3 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{-1}\color{blue}{+1+14x } & = & -3 \color{red}{ -14x }\color{blue}{+1+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & -3 \color{blue}{+1} \\\Leftrightarrow &19x & = &-2\\\Leftrightarrow & \color{red}{19}x & = &-2\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-2}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{19} } & & \\ & V = \left\{ \frac{-2}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{-15}& = & -2 \color{red}{ +8x } \\\Leftrightarrow & -13x \color{red}{-15}\color{blue}{+15-8x } & = & -2 \color{red}{ +8x }\color{blue}{+15-8x } \\\Leftrightarrow & -13x \color{blue}{-8x } & = & -2 \color{blue}{+15} \\\Leftrightarrow &-21x & = &13\\\Leftrightarrow & \color{red}{-21}x & = &13\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{13}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{21} } & & \\ & V = \left\{ \frac{-13}{21} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{+8}& = & 3 \color{red}{ -7x } \\\Leftrightarrow & 11x \color{red}{+8}\color{blue}{-8+7x } & = & 3 \color{red}{ -7x }\color{blue}{-8+7x } \\\Leftrightarrow & 11x \color{blue}{+7x } & = & 3 \color{blue}{-8} \\\Leftrightarrow &18x & = &-5\\\Leftrightarrow & \color{red}{18}x & = &-5\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}} & = & \frac{-5}{18} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{18} } & & \\ & V = \left\{ \frac{-5}{18} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{-13}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-13}\color{blue}{+13-x } & = & -11 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -11 \color{blue}{+13} \\\Leftrightarrow &-7x & = &2\\\Leftrightarrow & \color{red}{-7}x & = &2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{-4}& = & 12 \color{red}{ +14x } \\\Leftrightarrow & 13x \color{red}{-4}\color{blue}{+4-14x } & = & 12 \color{red}{ +14x }\color{blue}{+4-14x } \\\Leftrightarrow & 13x \color{blue}{-14x } & = & 12 \color{blue}{+4} \\\Leftrightarrow &-x & = &16\\\Leftrightarrow & \color{red}{-}x & = &16\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{16}{-1} \\\Leftrightarrow & \color{green}{ x = -16 } & & \\ & V = \left\{ -16 \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{-6}& = & -5 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-6}\color{blue}{+6-x } & = & -5 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & -5 \color{blue}{+6} \\\Leftrightarrow &9x & = &1\\\Leftrightarrow & \color{red}{9}x & = &1\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{1}{9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{-15}& = & 4 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-15}\color{blue}{+15-13x } & = & 4 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 4 \color{blue}{+15} \\\Leftrightarrow &-25x & = &19\\\Leftrightarrow & \color{red}{-25}x & = &19\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{19}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{25} } & & \\ & V = \left\{ \frac{-19}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{+13}& = & -2 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{+13}\color{blue}{-13+12x } & = & -2 \color{red}{ -12x }\color{blue}{-13+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & -2 \color{blue}{-13} \\\Leftrightarrow &25x & = &-15\\\Leftrightarrow & \color{red}{25}x & = &-15\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-15}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{-4}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{-4}\color{blue}{+4-11x } & = & -3 \color{red}{ +11x }\color{blue}{+4-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & -3 \color{blue}{+4} \\\Leftrightarrow &-9x & = &1\\\Leftrightarrow & \color{red}{-9}x & = &1\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{1}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{9} } & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)