Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{+8}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+8}\color{blue}{-8-x } & = & -1 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -1 \color{blue}{-8} \\\Leftrightarrow &-14x & = &-9\\\Leftrightarrow & \color{red}{-14}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-9}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{9}{14} } & & \\ & V = \left\{ \frac{9}{14} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{+9}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+9}\color{blue}{-9-x } & = & -8 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -8 \color{blue}{-9} \\\Leftrightarrow &-9x & = &-17\\\Leftrightarrow & \color{red}{-9}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-17}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{17}{9} } & & \\ & V = \left\{ \frac{17}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{+9}& = & -4 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{+9}\color{blue}{-9+7x } & = & -4 \color{red}{ -7x }\color{blue}{-9+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & -4 \color{blue}{-9} \\\Leftrightarrow &22x & = &-13\\\Leftrightarrow & \color{red}{22}x & = &-13\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-13}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{22} } & & \\ & V = \left\{ \frac{-13}{22} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{-4}& = & -15 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{-4}\color{blue}{+4+3x } & = & -15 \color{red}{ -3x }\color{blue}{+4+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & -15 \color{blue}{+4} \\\Leftrightarrow &7x & = &-11\\\Leftrightarrow & \color{red}{7}x & = &-11\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-11}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{7} } & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{+5}& = & -8 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+5}\color{blue}{-5+11x } & = & -8 \color{red}{ -11x }\color{blue}{-5+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & -8 \color{blue}{-5} \\\Leftrightarrow &15x & = &-13\\\Leftrightarrow & \color{red}{15}x & = &-13\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-13}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{15} } & & \\ & V = \left\{ \frac{-13}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{+15}& = & 1 \color{red}{ +3x } \\\Leftrightarrow & -11x \color{red}{+15}\color{blue}{-15-3x } & = & 1 \color{red}{ +3x }\color{blue}{-15-3x } \\\Leftrightarrow & -11x \color{blue}{-3x } & = & 1 \color{blue}{-15} \\\Leftrightarrow &-14x & = &-14\\\Leftrightarrow & \color{red}{-14}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-14}{-14} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{+3}& = & 10 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{+3}\color{blue}{-3+11x } & = & 10 \color{red}{ -11x }\color{blue}{-3+11x } \\\Leftrightarrow & 14x \color{blue}{+11x } & = & 10 \color{blue}{-3} \\\Leftrightarrow &25x & = &7\\\Leftrightarrow & \color{red}{25}x & = &7\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{7}{25} \\\Leftrightarrow & \color{green}{ x = \frac{7}{25} } & & \\ & V = \left\{ \frac{7}{25} \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{+9}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+9}\color{blue}{-9-x } & = & -14 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -14 \color{blue}{-9} \\\Leftrightarrow &-4x & = &-23\\\Leftrightarrow & \color{red}{-4}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-23}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{23}{4} } & & \\ & V = \left\{ \frac{23}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{-5}& = & -4 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-5}\color{blue}{+5+2x } & = & -4 \color{red}{ -2x }\color{blue}{+5+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -4 \color{blue}{+5} \\\Leftrightarrow &17x & = &1\\\Leftrightarrow & \color{red}{17}x & = &1\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{1}{17} \\\Leftrightarrow & \color{green}{ x = \frac{1}{17} } & & \\ & V = \left\{ \frac{1}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{-12}& = & -15 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{-12}\color{blue}{+12-3x } & = & -15 \color{red}{ +3x }\color{blue}{+12-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & -15 \color{blue}{+12} \\\Leftrightarrow &-x & = &-3\\\Leftrightarrow & \color{red}{-}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-3}{-1} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{-13}& = & -3 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{-13}\color{blue}{+13+5x } & = & -3 \color{red}{ -5x }\color{blue}{+13+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & -3 \color{blue}{+13} \\\Leftrightarrow &11x & = &10\\\Leftrightarrow & \color{red}{11}x & = &10\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{10}{11} \\\Leftrightarrow & \color{green}{ x = \frac{10}{11} } & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{-11}& = & 7 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-11}\color{blue}{+11-13x } & = & 7 \color{red}{ +13x }\color{blue}{+11-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 7 \color{blue}{+11} \\\Leftrightarrow &-25x & = &18\\\Leftrightarrow & \color{red}{-25}x & = &18\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{18}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{25} } & & \\ & V = \left\{ \frac{-18}{25} \right\} & \\\end{align}\)