Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{-11}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-11}\color{blue}{+11-x } & = & -4 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -4 \color{blue}{+11} \\\Leftrightarrow &-14x & = &7\\\Leftrightarrow & \color{red}{-14}x & = &7\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{7}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-4}& = & -11 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-4}\color{blue}{+4+11x } & = & -11 \color{red}{ -11x }\color{blue}{+4+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -11 \color{blue}{+4} \\\Leftrightarrow &23x & = &-7\\\Leftrightarrow & \color{red}{23}x & = &-7\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-7}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{23} } & & \\ & V = \left\{ \frac{-7}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{-6}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-6}\color{blue}{+6-x } & = & -12 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -12 \color{blue}{+6} \\\Leftrightarrow &-9x & = &-6\\\Leftrightarrow & \color{red}{-9}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{-15}& = & 2 \color{red}{ +5x } \\\Leftrightarrow & 8x \color{red}{-15}\color{blue}{+15-5x } & = & 2 \color{red}{ +5x }\color{blue}{+15-5x } \\\Leftrightarrow & 8x \color{blue}{-5x } & = & 2 \color{blue}{+15} \\\Leftrightarrow &3x & = &17\\\Leftrightarrow & \color{red}{3}x & = &17\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{17}{3} \\\Leftrightarrow & \color{green}{ x = \frac{17}{3} } & & \\ & V = \left\{ \frac{17}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{+9}& = & 9 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{+9}\color{blue}{-9+3x } & = & 9 \color{red}{ -3x }\color{blue}{-9+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & 9 \color{blue}{-9} \\\Leftrightarrow &10x & = &0\\\Leftrightarrow & \color{red}{10}x & = &0\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{0}{10} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{-3}& = & 2 \color{red}{ +3x } \\\Leftrightarrow & 8x \color{red}{-3}\color{blue}{+3-3x } & = & 2 \color{red}{ +3x }\color{blue}{+3-3x } \\\Leftrightarrow & 8x \color{blue}{-3x } & = & 2 \color{blue}{+3} \\\Leftrightarrow &5x & = &5\\\Leftrightarrow & \color{red}{5}x & = &5\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{5}{5} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{+8}& = & 13 \color{red}{ +5x } \\\Leftrightarrow & -14x \color{red}{+8}\color{blue}{-8-5x } & = & 13 \color{red}{ +5x }\color{blue}{-8-5x } \\\Leftrightarrow & -14x \color{blue}{-5x } & = & 13 \color{blue}{-8} \\\Leftrightarrow &-19x & = &5\\\Leftrightarrow & \color{red}{-19}x & = &5\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{5}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{19} } & & \\ & V = \left\{ \frac{-5}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{+4}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+4}\color{blue}{-4-x } & = & -3 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -3 \color{blue}{-4} \\\Leftrightarrow &-15x & = &-7\\\Leftrightarrow & \color{red}{-15}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-7}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{15} } & & \\ & V = \left\{ \frac{7}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{-1}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-1}\color{blue}{+1-x } & = & 13 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 13 \color{blue}{+1} \\\Leftrightarrow &5x & = &14\\\Leftrightarrow & \color{red}{5}x & = &14\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{14}{5} \\\Leftrightarrow & \color{green}{ x = \frac{14}{5} } & & \\ & V = \left\{ \frac{14}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{+14}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+14}\color{blue}{-14-x } & = & -11 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -11 \color{blue}{-14} \\\Leftrightarrow &-9x & = &-25\\\Leftrightarrow & \color{red}{-9}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-25}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{25}{9} } & & \\ & V = \left\{ \frac{25}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{-13}& = & 7 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{-13}\color{blue}{+13+12x } & = & 7 \color{red}{ -12x }\color{blue}{+13+12x } \\\Leftrightarrow & 5x \color{blue}{+12x } & = & 7 \color{blue}{+13} \\\Leftrightarrow &17x & = &20\\\Leftrightarrow & \color{red}{17}x & = &20\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{20}{17} \\\Leftrightarrow & \color{green}{ x = \frac{20}{17} } & & \\ & V = \left\{ \frac{20}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{+15}& = & -12 \color{red}{ -12x } \\\Leftrightarrow & x \color{red}{+15}\color{blue}{-15+12x } & = & -12 \color{red}{ -12x }\color{blue}{-15+12x } \\\Leftrightarrow & x \color{blue}{+12x } & = & -12 \color{blue}{-15} \\\Leftrightarrow &13x & = &-27\\\Leftrightarrow & \color{red}{13}x & = &-27\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-27}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{13} } & & \\ & V = \left\{ \frac{-27}{13} \right\} & \\\end{align}\)