Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{+6}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+6}\color{blue}{-6-x } & = & 7 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 7 \color{blue}{-6} \\\Leftrightarrow &-12x & = &1\\\Leftrightarrow & \color{red}{-12}x & = &1\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{1}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{12} } & & \\ & V = \left\{ \frac{-1}{12} \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{-3}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-3}\color{blue}{+3-x } & = & -8 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -8 \color{blue}{+3} \\\Leftrightarrow &-4x & = &-5\\\Leftrightarrow & \color{red}{-4}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-5}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{+5}& = & 10 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{+5}\color{blue}{-5+4x } & = & 10 \color{red}{ -4x }\color{blue}{-5+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & 10 \color{blue}{-5} \\\Leftrightarrow &13x & = &5\\\Leftrightarrow & \color{red}{13}x & = &5\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{5}{13} \\\Leftrightarrow & \color{green}{ x = \frac{5}{13} } & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{+4}& = & 3 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+4}\color{blue}{-4+2x } & = & 3 \color{red}{ -2x }\color{blue}{-4+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 3 \color{blue}{-4} \\\Leftrightarrow &17x & = &-1\\\Leftrightarrow & \color{red}{17}x & = &-1\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-1}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{17} } & & \\ & V = \left\{ \frac{-1}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{+9}& = & -13 \color{red}{ -8x } \\\Leftrightarrow & -x \color{red}{+9}\color{blue}{-9+8x } & = & -13 \color{red}{ -8x }\color{blue}{-9+8x } \\\Leftrightarrow & -x \color{blue}{+8x } & = & -13 \color{blue}{-9} \\\Leftrightarrow &7x & = &-22\\\Leftrightarrow & \color{red}{7}x & = &-22\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-22}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{7} } & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{-9}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-9}\color{blue}{+9-x } & = & -3 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -3 \color{blue}{+9} \\\Leftrightarrow &-5x & = &6\\\Leftrightarrow & \color{red}{-5}x & = &6\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{6}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{+1}& = & 14 \color{red}{ +14x } \\\Leftrightarrow & -x \color{red}{+1}\color{blue}{-1-14x } & = & 14 \color{red}{ +14x }\color{blue}{-1-14x } \\\Leftrightarrow & -x \color{blue}{-14x } & = & 14 \color{blue}{-1} \\\Leftrightarrow &-15x & = &13\\\Leftrightarrow & \color{red}{-15}x & = &13\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{13}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{15} } & & \\ & V = \left\{ \frac{-13}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{+7}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+7}\color{blue}{-7-x } & = & -13 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -13 \color{blue}{-7} \\\Leftrightarrow &-10x & = &-20\\\Leftrightarrow & \color{red}{-10}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-20}{-10} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{+12}& = & -9 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{+12}\color{blue}{-12-13x } & = & -9 \color{red}{ +13x }\color{blue}{-12-13x } \\\Leftrightarrow & 12x \color{blue}{-13x } & = & -9 \color{blue}{-12} \\\Leftrightarrow &-x & = &-21\\\Leftrightarrow & \color{red}{-}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-21}{-1} \\\Leftrightarrow & \color{green}{ x = 21 } & & \\ & V = \left\{ 21 \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{-1}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & 4x \color{red}{-1}\color{blue}{+1-13x } & = & 13 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & 4x \color{blue}{-13x } & = & 13 \color{blue}{+1} \\\Leftrightarrow &-9x & = &14\\\Leftrightarrow & \color{red}{-9}x & = &14\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{14}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{9} } & & \\ & V = \left\{ \frac{-14}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{-10}& = & -7 \color{red}{ +14x } \\\Leftrightarrow & 11x \color{red}{-10}\color{blue}{+10-14x } & = & -7 \color{red}{ +14x }\color{blue}{+10-14x } \\\Leftrightarrow & 11x \color{blue}{-14x } & = & -7 \color{blue}{+10} \\\Leftrightarrow &-3x & = &3\\\Leftrightarrow & \color{red}{-3}x & = &3\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{3}{-3} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{-13}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-13}\color{blue}{+13-x } & = & 9 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 9 \color{blue}{+13} \\\Leftrightarrow &-10x & = &22\\\Leftrightarrow & \color{red}{-10}x & = &22\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{22}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{5} } & & \\ & V = \left\{ \frac{-11}{5} \right\} & \\\end{align}\)