Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{+4}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+4}\color{blue}{-4-x } & = & 5 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 5 \color{blue}{-4} \\\Leftrightarrow &-5x & = &1\\\Leftrightarrow & \color{red}{-5}x & = &1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{-13}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-13}\color{blue}{+13-x } & = & 10 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 10 \color{blue}{+13} \\\Leftrightarrow &-14x & = &23\\\Leftrightarrow & \color{red}{-14}x & = &23\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{23}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{14} } & & \\ & V = \left\{ \frac{-23}{14} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{+10}& = & 11 \color{red}{ +6x } \\\Leftrightarrow & 5x \color{red}{+10}\color{blue}{-10-6x } & = & 11 \color{red}{ +6x }\color{blue}{-10-6x } \\\Leftrightarrow & 5x \color{blue}{-6x } & = & 11 \color{blue}{-10} \\\Leftrightarrow &-x & = &1\\\Leftrightarrow & \color{red}{-}x & = &1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{1}{-1} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{-13}& = & 12 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{-13}\color{blue}{+13+4x } & = & 12 \color{red}{ -4x }\color{blue}{+13+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & 12 \color{blue}{+13} \\\Leftrightarrow &9x & = &25\\\Leftrightarrow & \color{red}{9}x & = &25\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{25}{9} \\\Leftrightarrow & \color{green}{ x = \frac{25}{9} } & & \\ & V = \left\{ \frac{25}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{+9}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+9}\color{blue}{-9-x } & = & 8 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 8 \color{blue}{-9} \\\Leftrightarrow &-8x & = &-1\\\Leftrightarrow & \color{red}{-8}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{-3}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-3}\color{blue}{+3-7x } & = & 11 \color{red}{ +7x }\color{blue}{+3-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 11 \color{blue}{+3} \\\Leftrightarrow &-17x & = &14\\\Leftrightarrow & \color{red}{-17}x & = &14\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{14}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{17} } & & \\ & V = \left\{ \frac{-14}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{+13}& = & -7 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{+13}\color{blue}{-13-3x } & = & -7 \color{red}{ +3x }\color{blue}{-13-3x } \\\Leftrightarrow & -2x \color{blue}{-3x } & = & -7 \color{blue}{-13} \\\Leftrightarrow &-5x & = &-20\\\Leftrightarrow & \color{red}{-5}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-20}{-5} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{-4}& = & 4 \color{red}{ -7x } \\\Leftrightarrow & 5x \color{red}{-4}\color{blue}{+4+7x } & = & 4 \color{red}{ -7x }\color{blue}{+4+7x } \\\Leftrightarrow & 5x \color{blue}{+7x } & = & 4 \color{blue}{+4} \\\Leftrightarrow &12x & = &8\\\Leftrightarrow & \color{red}{12}x & = &8\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{8}{12} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{-1}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-1}\color{blue}{+1-x } & = & -9 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -9 \color{blue}{+1} \\\Leftrightarrow &-9x & = &-8\\\Leftrightarrow & \color{red}{-9}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-8}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{8}{9} } & & \\ & V = \left\{ \frac{8}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{-8}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-8}\color{blue}{+8-x } & = & -8 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -8 \color{blue}{+8} \\\Leftrightarrow &-15x & = &0\\\Leftrightarrow & \color{red}{-15}x & = &0\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{0}{-15} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{-14}& = & 7 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{-14}\color{blue}{+14-7x } & = & 7 \color{red}{ +7x }\color{blue}{+14-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & 7 \color{blue}{+14} \\\Leftrightarrow &8x & = &21\\\Leftrightarrow & \color{red}{8}x & = &21\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{21}{8} \\\Leftrightarrow & \color{green}{ x = \frac{21}{8} } & & \\ & V = \left\{ \frac{21}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{+7}& = & -1 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+7}\color{blue}{-7+3x } & = & -1 \color{red}{ -3x }\color{blue}{-7+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -1 \color{blue}{-7} \\\Leftrightarrow &13x & = &-8\\\Leftrightarrow & \color{red}{13}x & = &-8\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-8}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{13} } & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)