Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{-7}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-7}\color{blue}{+7-7x } & = & -7 \color{red}{ +7x }\color{blue}{+7-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -7 \color{blue}{+7} \\\Leftrightarrow &-20x & = &0\\\Leftrightarrow & \color{red}{-20}x & = &0\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{0}{-20} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{+5}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+5}\color{blue}{-5-x } & = & 5 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 5 \color{blue}{-5} \\\Leftrightarrow &-15x & = &0\\\Leftrightarrow & \color{red}{-15}x & = &0\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{0}{-15} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{+13}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+13}\color{blue}{-13-x } & = & 6 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 6 \color{blue}{-13} \\\Leftrightarrow &-5x & = &-7\\\Leftrightarrow & \color{red}{-5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{-15}& = & 12 \color{red}{ -5x } \\\Leftrightarrow & -x \color{red}{-15}\color{blue}{+15+5x } & = & 12 \color{red}{ -5x }\color{blue}{+15+5x } \\\Leftrightarrow & -x \color{blue}{+5x } & = & 12 \color{blue}{+15} \\\Leftrightarrow &4x & = &27\\\Leftrightarrow & \color{red}{4}x & = &27\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{27}{4} \\\Leftrightarrow & \color{green}{ x = \frac{27}{4} } & & \\ & V = \left\{ \frac{27}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{+5}& = & 2 \color{red}{ +13x } \\\Leftrightarrow & 15x \color{red}{+5}\color{blue}{-5-13x } & = & 2 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & 15x \color{blue}{-13x } & = & 2 \color{blue}{-5} \\\Leftrightarrow &2x & = &-3\\\Leftrightarrow & \color{red}{2}x & = &-3\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-3}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{-8}& = & -13 \color{red}{ +13x } \\\Leftrightarrow & 4x \color{red}{-8}\color{blue}{+8-13x } & = & -13 \color{red}{ +13x }\color{blue}{+8-13x } \\\Leftrightarrow & 4x \color{blue}{-13x } & = & -13 \color{blue}{+8} \\\Leftrightarrow &-9x & = &-5\\\Leftrightarrow & \color{red}{-9}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-5}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{9} } & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{-15}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-15}\color{blue}{+15-x } & = & -15 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -15 \color{blue}{+15} \\\Leftrightarrow &-15x & = &0\\\Leftrightarrow & \color{red}{-15}x & = &0\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{0}{-15} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{-12}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-12}\color{blue}{+12-x } & = & 7 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 7 \color{blue}{+12} \\\Leftrightarrow &-6x & = &19\\\Leftrightarrow & \color{red}{-6}x & = &19\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{19}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{6} } & & \\ & V = \left\{ \frac{-19}{6} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{+2}& = & -6 \color{red}{ +13x } \\\Leftrightarrow & 15x \color{red}{+2}\color{blue}{-2-13x } & = & -6 \color{red}{ +13x }\color{blue}{-2-13x } \\\Leftrightarrow & 15x \color{blue}{-13x } & = & -6 \color{blue}{-2} \\\Leftrightarrow &2x & = &-8\\\Leftrightarrow & \color{red}{2}x & = &-8\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-8}{2} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{-3}& = & -11 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{-3}\color{blue}{+3-5x } & = & -11 \color{red}{ +5x }\color{blue}{+3-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -11 \color{blue}{+3} \\\Leftrightarrow &7x & = &-8\\\Leftrightarrow & \color{red}{7}x & = &-8\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-8}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{+10}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+10}\color{blue}{-10-x } & = & -5 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -5 \color{blue}{-10} \\\Leftrightarrow &-4x & = &-15\\\Leftrightarrow & \color{red}{-4}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-15}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{15}{4} } & & \\ & V = \left\{ \frac{15}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{-13}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-13}\color{blue}{+13-x } & = & -6 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -6 \color{blue}{+13} \\\Leftrightarrow &-11x & = &7\\\Leftrightarrow & \color{red}{-11}x & = &7\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{7}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)