Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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