Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{+5}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+5}\color{blue}{-5-x } & = & -9 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -9 \color{blue}{-5} \\\Leftrightarrow &-15x & = &-14\\\Leftrightarrow & \color{red}{-15}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-14}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{14}{15} } & & \\ & V = \left\{ \frac{14}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{-14}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-14}\color{blue}{+14-x } & = & -6 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -6 \color{blue}{+14} \\\Leftrightarrow &-12x & = &8\\\Leftrightarrow & \color{red}{-12}x & = &8\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{8}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{+11}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+11}\color{blue}{-11-x } & = & 2 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 2 \color{blue}{-11} \\\Leftrightarrow &-13x & = &-9\\\Leftrightarrow & \color{red}{-13}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-9}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{9}{13} } & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{-12}& = & -8 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-12}\color{blue}{+12-7x } & = & -8 \color{red}{ +7x }\color{blue}{+12-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -8 \color{blue}{+12} \\\Leftrightarrow &-17x & = &4\\\Leftrightarrow & \color{red}{-17}x & = &4\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{4}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{17} } & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{-3}& = & -9 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{-3}\color{blue}{+3+7x } & = & -9 \color{red}{ -7x }\color{blue}{+3+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & -9 \color{blue}{+3} \\\Leftrightarrow &11x & = &-6\\\Leftrightarrow & \color{red}{11}x & = &-6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{+8}& = & 4 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+8}\color{blue}{-8-13x } & = & 4 \color{red}{ +13x }\color{blue}{-8-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 4 \color{blue}{-8} \\\Leftrightarrow &-25x & = &-4\\\Leftrightarrow & \color{red}{-25}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-4}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{4}{25} } & & \\ & V = \left\{ \frac{4}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{-6}& = & 14 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{-6}\color{blue}{+6+3x } & = & 14 \color{red}{ -3x }\color{blue}{+6+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & 14 \color{blue}{+6} \\\Leftrightarrow &10x & = &20\\\Leftrightarrow & \color{red}{10}x & = &20\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{20}{10} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{+1}& = & -5 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{+1}\color{blue}{-1-x } & = & -5 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & -5 \color{blue}{-1} \\\Leftrightarrow &12x & = &-6\\\Leftrightarrow & \color{red}{12}x & = &-6\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-6}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{-7}& = & 11 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{-7}\color{blue}{+7+2x } & = & 11 \color{red}{ -2x }\color{blue}{+7+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & 11 \color{blue}{+7} \\\Leftrightarrow &5x & = &18\\\Leftrightarrow & \color{red}{5}x & = &18\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{18}{5} \\\Leftrightarrow & \color{green}{ x = \frac{18}{5} } & & \\ & V = \left\{ \frac{18}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{-5}& = & 12 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-5}\color{blue}{+5-7x } & = & 12 \color{red}{ +7x }\color{blue}{+5-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 12 \color{blue}{+5} \\\Leftrightarrow &-17x & = &17\\\Leftrightarrow & \color{red}{-17}x & = &17\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{17}{-17} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{-2}& = & -1 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-2}\color{blue}{+2-13x } & = & -1 \color{red}{ +13x }\color{blue}{+2-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -1 \color{blue}{+2} \\\Leftrightarrow &-28x & = &1\\\Leftrightarrow & \color{red}{-28}x & = &1\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{1}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{28} } & & \\ & V = \left\{ \frac{-1}{28} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{+6}& = & -11 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{+6}\color{blue}{-6+13x } & = & -11 \color{red}{ -13x }\color{blue}{-6+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & -11 \color{blue}{-6} \\\Leftrightarrow &22x & = &-17\\\Leftrightarrow & \color{red}{22}x & = &-17\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-17}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{22} } & & \\ & V = \left\{ \frac{-17}{22} \right\} & \\\end{align}\)