Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{-9}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-9}\color{blue}{+9-x } & = & -12 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -12 \color{blue}{+9} \\\Leftrightarrow &-14x & = &-3\\\Leftrightarrow & \color{red}{-14}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-3}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{14} } & & \\ & V = \left\{ \frac{3}{14} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{-1}& = & 6 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{-1}\color{blue}{+1+5x } & = & 6 \color{red}{ -5x }\color{blue}{+1+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & 6 \color{blue}{+1} \\\Leftrightarrow &8x & = &7\\\Leftrightarrow & \color{red}{8}x & = &7\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{7}{8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{+12}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+12}\color{blue}{-12-x } & = & 5 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 5 \color{blue}{-12} \\\Leftrightarrow &-9x & = &-7\\\Leftrightarrow & \color{red}{-9}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{9} } & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{+14}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+14}\color{blue}{-14-x } & = & -3 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -3 \color{blue}{-14} \\\Leftrightarrow &-14x & = &-17\\\Leftrightarrow & \color{red}{-14}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-17}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{17}{14} } & & \\ & V = \left\{ \frac{17}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{-9}& = & -9 \color{red}{ +15x } \\\Leftrightarrow & x \color{red}{-9}\color{blue}{+9-15x } & = & -9 \color{red}{ +15x }\color{blue}{+9-15x } \\\Leftrightarrow & x \color{blue}{-15x } & = & -9 \color{blue}{+9} \\\Leftrightarrow &-14x & = &0\\\Leftrightarrow & \color{red}{-14}x & = &0\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{0}{-14} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{-15}& = & -4 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-15}\color{blue}{+15-7x } & = & -4 \color{red}{ +7x }\color{blue}{+15-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -4 \color{blue}{+15} \\\Leftrightarrow &-20x & = &11\\\Leftrightarrow & \color{red}{-20}x & = &11\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{11}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{20} } & & \\ & V = \left\{ \frac{-11}{20} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{+10}& = & -1 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{+10}\color{blue}{-10+11x } & = & -1 \color{red}{ -11x }\color{blue}{-10+11x } \\\Leftrightarrow & 14x \color{blue}{+11x } & = & -1 \color{blue}{-10} \\\Leftrightarrow &25x & = &-11\\\Leftrightarrow & \color{red}{25}x & = &-11\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-11}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{25} } & & \\ & V = \left\{ \frac{-11}{25} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{-13}& = & 15 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{-13}\color{blue}{+13+7x } & = & 15 \color{red}{ -7x }\color{blue}{+13+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & 15 \color{blue}{+13} \\\Leftrightarrow &11x & = &28\\\Leftrightarrow & \color{red}{11}x & = &28\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{28}{11} \\\Leftrightarrow & \color{green}{ x = \frac{28}{11} } & & \\ & V = \left\{ \frac{28}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{-12}& = & 12 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{-12}\color{blue}{+12+9x } & = & 12 \color{red}{ -9x }\color{blue}{+12+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & 12 \color{blue}{+12} \\\Leftrightarrow &14x & = &24\\\Leftrightarrow & \color{red}{14}x & = &24\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{24}{14} \\\Leftrightarrow & \color{green}{ x = \frac{12}{7} } & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{+5}& = & 5 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+5}\color{blue}{-5-x } & = & 5 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 5 \color{blue}{-5} \\\Leftrightarrow &5x & = &0\\\Leftrightarrow & \color{red}{5}x & = &0\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{0}{5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{-11}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-11}\color{blue}{+11-x } & = & 14 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 14 \color{blue}{+11} \\\Leftrightarrow &-5x & = &25\\\Leftrightarrow & \color{red}{-5}x & = &25\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{25}{-5} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{-3}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-3}\color{blue}{+3-x } & = & -8 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -8 \color{blue}{+3} \\\Leftrightarrow &-6x & = &-5\\\Leftrightarrow & \color{red}{-6}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-5}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)