Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{+13}& = & 12 \color{red}{ +8x } \\\Leftrightarrow & 11x \color{red}{+13}\color{blue}{-13-8x } & = & 12 \color{red}{ +8x }\color{blue}{-13-8x } \\\Leftrightarrow & 11x \color{blue}{-8x } & = & 12 \color{blue}{-13} \\\Leftrightarrow &3x & = &-1\\\Leftrightarrow & \color{red}{3}x & = &-1\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-1}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{-10}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-10}\color{blue}{+10-x } & = & -9 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -9 \color{blue}{+10} \\\Leftrightarrow &-14x & = &1\\\Leftrightarrow & \color{red}{-14}x & = &1\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{1}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{14} } & & \\ & V = \left\{ \frac{-1}{14} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{+14}& = & -8 \color{red}{ +7x } \\\Leftrightarrow & 4x \color{red}{+14}\color{blue}{-14-7x } & = & -8 \color{red}{ +7x }\color{blue}{-14-7x } \\\Leftrightarrow & 4x \color{blue}{-7x } & = & -8 \color{blue}{-14} \\\Leftrightarrow &-3x & = &-22\\\Leftrightarrow & \color{red}{-3}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-22}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{22}{3} } & & \\ & V = \left\{ \frac{22}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{+10}& = & -10 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{+10}\color{blue}{-10-12x } & = & -10 \color{red}{ +12x }\color{blue}{-10-12x } \\\Leftrightarrow & 11x \color{blue}{-12x } & = & -10 \color{blue}{-10} \\\Leftrightarrow &-x & = &-20\\\Leftrightarrow & \color{red}{-}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-20}{-1} \\\Leftrightarrow & \color{green}{ x = 20 } & & \\ & V = \left\{ 20 \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{-13}& = & -12 \color{red}{ -7x } \\\Leftrightarrow & 11x \color{red}{-13}\color{blue}{+13+7x } & = & -12 \color{red}{ -7x }\color{blue}{+13+7x } \\\Leftrightarrow & 11x \color{blue}{+7x } & = & -12 \color{blue}{+13} \\\Leftrightarrow &18x & = &1\\\Leftrightarrow & \color{red}{18}x & = &1\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}} & = & \frac{1}{18} \\\Leftrightarrow & \color{green}{ x = \frac{1}{18} } & & \\ & V = \left\{ \frac{1}{18} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{-11}& = & 4 \color{red}{ +12x } \\\Leftrightarrow & 7x \color{red}{-11}\color{blue}{+11-12x } & = & 4 \color{red}{ +12x }\color{blue}{+11-12x } \\\Leftrightarrow & 7x \color{blue}{-12x } & = & 4 \color{blue}{+11} \\\Leftrightarrow &-5x & = &15\\\Leftrightarrow & \color{red}{-5}x & = &15\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{15}{-5} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{-3}& = & 10 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{-3}\color{blue}{+3+9x } & = & 10 \color{red}{ -9x }\color{blue}{+3+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & 10 \color{blue}{+3} \\\Leftrightarrow &14x & = &13\\\Leftrightarrow & \color{red}{14}x & = &13\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{13}{14} \\\Leftrightarrow & \color{green}{ x = \frac{13}{14} } & & \\ & V = \left\{ \frac{13}{14} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{+11}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+11}\color{blue}{-11-x } & = & 13 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 13 \color{blue}{-11} \\\Leftrightarrow &-15x & = &2\\\Leftrightarrow & \color{red}{-15}x & = &2\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{2}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{15} } & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{+11}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+11}\color{blue}{-11-x } & = & 1 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 1 \color{blue}{-11} \\\Leftrightarrow &-16x & = &-10\\\Leftrightarrow & \color{red}{-16}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-10}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{-6}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-6}\color{blue}{+6-x } & = & 6 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 6 \color{blue}{+6} \\\Leftrightarrow &-15x & = &12\\\Leftrightarrow & \color{red}{-15}x & = &12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{+9}& = & -7 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+9}\color{blue}{-9+13x } & = & -7 \color{red}{ -13x }\color{blue}{-9+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & -7 \color{blue}{-9} \\\Leftrightarrow &24x & = &-16\\\Leftrightarrow & \color{red}{24}x & = &-16\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-16}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{-9}& = & -15 \color{red}{ +8x } \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9-8x } & = & -15 \color{red}{ +8x }\color{blue}{+9-8x } \\\Leftrightarrow & -5x \color{blue}{-8x } & = & -15 \color{blue}{+9} \\\Leftrightarrow &-13x & = &-6\\\Leftrightarrow & \color{red}{-13}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{6}{13} } & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)