Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{+15}& = & -1 \color{red}{ +11x } \\\Leftrightarrow & x \color{red}{+15}\color{blue}{-15-11x } & = & -1 \color{red}{ +11x }\color{blue}{-15-11x } \\\Leftrightarrow & x \color{blue}{-11x } & = & -1 \color{blue}{-15} \\\Leftrightarrow &-10x & = &-16\\\Leftrightarrow & \color{red}{-10}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-16}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{+14}& = & -14 \color{red}{ +12x } \\\Leftrightarrow & 7x \color{red}{+14}\color{blue}{-14-12x } & = & -14 \color{red}{ +12x }\color{blue}{-14-12x } \\\Leftrightarrow & 7x \color{blue}{-12x } & = & -14 \color{blue}{-14} \\\Leftrightarrow &-5x & = &-28\\\Leftrightarrow & \color{red}{-5}x & = &-28\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-28}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{28}{5} } & & \\ & V = \left\{ \frac{28}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{+14}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+14}\color{blue}{-14-x } & = & -11 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -11 \color{blue}{-14} \\\Leftrightarrow &-14x & = &-25\\\Leftrightarrow & \color{red}{-14}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-25}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{25}{14} } & & \\ & V = \left\{ \frac{25}{14} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{+14}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+14}\color{blue}{-14-x } & = & 14 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 14 \color{blue}{-14} \\\Leftrightarrow &-16x & = &0\\\Leftrightarrow & \color{red}{-16}x & = &0\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{0}{-16} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+14}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+14}\color{blue}{-14-x } & = & 14 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 14 \color{blue}{-14} \\\Leftrightarrow &-9x & = &0\\\Leftrightarrow & \color{red}{-9}x & = &0\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{0}{-9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{-13}& = & -8 \color{red}{ +2x } \\\Leftrightarrow & 5x \color{red}{-13}\color{blue}{+13-2x } & = & -8 \color{red}{ +2x }\color{blue}{+13-2x } \\\Leftrightarrow & 5x \color{blue}{-2x } & = & -8 \color{blue}{+13} \\\Leftrightarrow &3x & = &5\\\Leftrightarrow & \color{red}{3}x & = &5\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{5}{3} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{-10}& = & -3 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{-10}\color{blue}{+10+4x } & = & -3 \color{red}{ -4x }\color{blue}{+10+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & -3 \color{blue}{+10} \\\Leftrightarrow &9x & = &7\\\Leftrightarrow & \color{red}{9}x & = &7\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{7}{9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{9} } & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{+6}& = & -2 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{+6}\color{blue}{-6+3x } & = & -2 \color{red}{ -3x }\color{blue}{-6+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & -2 \color{blue}{-6} \\\Leftrightarrow &7x & = &-8\\\Leftrightarrow & \color{red}{7}x & = &-8\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-8}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -9x \color{red}{+2}& = & 3 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+2}\color{blue}{-2-5x } & = & 3 \color{red}{ +5x }\color{blue}{-2-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & 3 \color{blue}{-2} \\\Leftrightarrow &-14x & = &1\\\Leftrightarrow & \color{red}{-14}x & = &1\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{1}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{14} } & & \\ & V = \left\{ \frac{-1}{14} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{-2}& = & 10 \color{red}{ +3x } \\\Leftrightarrow & 11x \color{red}{-2}\color{blue}{+2-3x } & = & 10 \color{red}{ +3x }\color{blue}{+2-3x } \\\Leftrightarrow & 11x \color{blue}{-3x } & = & 10 \color{blue}{+2} \\\Leftrightarrow &8x & = &12\\\Leftrightarrow & \color{red}{8}x & = &12\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{12}{8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{+11}& = & -5 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{+11}\color{blue}{-11-13x } & = & -5 \color{red}{ +13x }\color{blue}{-11-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & -5 \color{blue}{-11} \\\Leftrightarrow &-3x & = &-16\\\Leftrightarrow & \color{red}{-3}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-16}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{16}{3} } & & \\ & V = \left\{ \frac{16}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{+12}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+12}\color{blue}{-12-x } & = & -10 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -10 \color{blue}{-12} \\\Leftrightarrow &-14x & = &-22\\\Leftrightarrow & \color{red}{-14}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-22}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{11}{7} } & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)