Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{+10}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+10}\color{blue}{-10-x } & = & 3 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 3 \color{blue}{-10} \\\Leftrightarrow &-12x & = &-7\\\Leftrightarrow & \color{red}{-12}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-7}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{12} } & & \\ & V = \left\{ \frac{7}{12} \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{-2}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-2}\color{blue}{+2-x } & = & 3 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 3 \color{blue}{+2} \\\Leftrightarrow &-4x & = &5\\\Leftrightarrow & \color{red}{-4}x & = &5\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{5}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{-14}& = & -8 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-14}\color{blue}{+14-13x } & = & -8 \color{red}{ +13x }\color{blue}{+14-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -8 \color{blue}{+14} \\\Leftrightarrow &-28x & = &6\\\Leftrightarrow & \color{red}{-28}x & = &6\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{6}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{14} } & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{+4}& = & -1 \color{red}{ +14x } \\\Leftrightarrow & 5x \color{red}{+4}\color{blue}{-4-14x } & = & -1 \color{red}{ +14x }\color{blue}{-4-14x } \\\Leftrightarrow & 5x \color{blue}{-14x } & = & -1 \color{blue}{-4} \\\Leftrightarrow &-9x & = &-5\\\Leftrightarrow & \color{red}{-9}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-5}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{9} } & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & -10x \color{red}{+3}& = & 3 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+3}\color{blue}{-3-7x } & = & 3 \color{red}{ +7x }\color{blue}{-3-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 3 \color{blue}{-3} \\\Leftrightarrow &-17x & = &0\\\Leftrightarrow & \color{red}{-17}x & = &0\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{0}{-17} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{+11}& = & -7 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+11}\color{blue}{-11-x } & = & -7 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -7 \color{blue}{-11} \\\Leftrightarrow &13x & = &-18\\\Leftrightarrow & \color{red}{13}x & = &-18\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-18}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{13} } & & \\ & V = \left\{ \frac{-18}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{+14}& = & -6 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+14}\color{blue}{-14+2x } & = & -6 \color{red}{ -2x }\color{blue}{-14+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -6 \color{blue}{-14} \\\Leftrightarrow &17x & = &-20\\\Leftrightarrow & \color{red}{17}x & = &-20\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-20}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{17} } & & \\ & V = \left\{ \frac{-20}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{+15}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+15}\color{blue}{-15-x } & = & 7 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 7 \color{blue}{-15} \\\Leftrightarrow &-9x & = &-8\\\Leftrightarrow & \color{red}{-9}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-8}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{8}{9} } & & \\ & V = \left\{ \frac{8}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{-6}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-6}\color{blue}{+6-x } & = & 6 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 6 \color{blue}{+6} \\\Leftrightarrow &-12x & = &12\\\Leftrightarrow & \color{red}{-12}x & = &12\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{12}{-12} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{+4}& = & 6 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+4}\color{blue}{-4-13x } & = & 6 \color{red}{ +13x }\color{blue}{-4-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 6 \color{blue}{-4} \\\Leftrightarrow &-28x & = &2\\\Leftrightarrow & \color{red}{-28}x & = &2\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{2}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{14} } & & \\ & V = \left\{ \frac{-1}{14} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{+14}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+14}\color{blue}{-14-x } & = & 7 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 7 \color{blue}{-14} \\\Leftrightarrow &-8x & = &-7\\\Leftrightarrow & \color{red}{-8}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-7}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{+14}& = & -5 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+14}\color{blue}{-14-x } & = & -5 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -5 \color{blue}{-14} \\\Leftrightarrow &13x & = &-19\\\Leftrightarrow & \color{red}{13}x & = &-19\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-19}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{13} } & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)