Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{-11}& = & 9 \color{red}{ -2x } \\\Leftrightarrow & x \color{red}{-11}\color{blue}{+11+2x } & = & 9 \color{red}{ -2x }\color{blue}{+11+2x } \\\Leftrightarrow & x \color{blue}{+2x } & = & 9 \color{blue}{+11} \\\Leftrightarrow &3x & = &20\\\Leftrightarrow & \color{red}{3}x & = &20\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{20}{3} \\\Leftrightarrow & \color{green}{ x = \frac{20}{3} } & & \\ & V = \left\{ \frac{20}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{+1}& = & -5 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+1}\color{blue}{-1-13x } & = & -5 \color{red}{ +13x }\color{blue}{-1-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -5 \color{blue}{-1} \\\Leftrightarrow &-25x & = &-6\\\Leftrightarrow & \color{red}{-25}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-6}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{6}{25} } & & \\ & V = \left\{ \frac{6}{25} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{-6}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-6}\color{blue}{+6-13x } & = & -7 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -7 \color{blue}{+6} \\\Leftrightarrow &-25x & = &-1\\\Leftrightarrow & \color{red}{-25}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-1}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{1}{25} } & & \\ & V = \left\{ \frac{1}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{-4}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & 8x \color{red}{-4}\color{blue}{+4-7x } & = & -7 \color{red}{ +7x }\color{blue}{+4-7x } \\\Leftrightarrow & 8x \color{blue}{-7x } & = & -7 \color{blue}{+4} \\\Leftrightarrow &x & = &-3\\\Leftrightarrow & \color{red}{}x & = &-3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -3 \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{+8}& = & -14 \color{red}{ +11x } \\\Leftrightarrow & 10x \color{red}{+8}\color{blue}{-8-11x } & = & -14 \color{red}{ +11x }\color{blue}{-8-11x } \\\Leftrightarrow & 10x \color{blue}{-11x } & = & -14 \color{blue}{-8} \\\Leftrightarrow &-x & = &-22\\\Leftrightarrow & \color{red}{-}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-22}{-1} \\\Leftrightarrow & \color{green}{ x = 22 } & & \\ & V = \left\{ 22 \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{+9}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+9}\color{blue}{-9-x } & = & -9 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -9 \color{blue}{-9} \\\Leftrightarrow &-8x & = &-18\\\Leftrightarrow & \color{red}{-8}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-18}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{+9}& = & 5 \color{red}{ +6x } \\\Leftrightarrow & x \color{red}{+9}\color{blue}{-9-6x } & = & 5 \color{red}{ +6x }\color{blue}{-9-6x } \\\Leftrightarrow & x \color{blue}{-6x } & = & 5 \color{blue}{-9} \\\Leftrightarrow &-5x & = &-4\\\Leftrightarrow & \color{red}{-5}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-4}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{+8}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{+8}\color{blue}{-8-x } & = & 8 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & 8 \color{blue}{-8} \\\Leftrightarrow &3x & = &0\\\Leftrightarrow & \color{red}{3}x & = &0\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{0}{3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & -9x \color{red}{-8}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-8}\color{blue}{+8-x } & = & 4 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 4 \color{blue}{+8} \\\Leftrightarrow &-10x & = &12\\\Leftrightarrow & \color{red}{-10}x & = &12\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{12}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{+9}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+9}\color{blue}{-9-x } & = & 10 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 10 \color{blue}{-9} \\\Leftrightarrow &-12x & = &1\\\Leftrightarrow & \color{red}{-12}x & = &1\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{1}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{12} } & & \\ & V = \left\{ \frac{-1}{12} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{-12}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-12}\color{blue}{+12-x } & = & -8 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -8 \color{blue}{+12} \\\Leftrightarrow &-14x & = &4\\\Leftrightarrow & \color{red}{-14}x & = &4\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{4}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{+6}& = & -7 \color{red}{ +2x } \\\Leftrightarrow & 9x \color{red}{+6}\color{blue}{-6-2x } & = & -7 \color{red}{ +2x }\color{blue}{-6-2x } \\\Leftrightarrow & 9x \color{blue}{-2x } & = & -7 \color{blue}{-6} \\\Leftrightarrow &7x & = &-13\\\Leftrightarrow & \color{red}{7}x & = &-13\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-13}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{7} } & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)