Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{+12}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+12}\color{blue}{-12-x } & = & -8 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -8 \color{blue}{-12} \\\Leftrightarrow &-11x & = &-20\\\Leftrightarrow & \color{red}{-11}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-20}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{20}{11} } & & \\ & V = \left\{ \frac{20}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{+2}& = & 7 \color{red}{ +5x } \\\Leftrightarrow & 14x \color{red}{+2}\color{blue}{-2-5x } & = & 7 \color{red}{ +5x }\color{blue}{-2-5x } \\\Leftrightarrow & 14x \color{blue}{-5x } & = & 7 \color{blue}{-2} \\\Leftrightarrow &9x & = &5\\\Leftrightarrow & \color{red}{9}x & = &5\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{5}{9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{9} } & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{+7}& = & -1 \color{red}{ +9x } \\\Leftrightarrow & 13x \color{red}{+7}\color{blue}{-7-9x } & = & -1 \color{red}{ +9x }\color{blue}{-7-9x } \\\Leftrightarrow & 13x \color{blue}{-9x } & = & -1 \color{blue}{-7} \\\Leftrightarrow &4x & = &-8\\\Leftrightarrow & \color{red}{4}x & = &-8\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-8}{4} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{+10}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+10}\color{blue}{-10-x } & = & -13 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -13 \color{blue}{-10} \\\Leftrightarrow &-12x & = &-23\\\Leftrightarrow & \color{red}{-12}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-23}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{23}{12} } & & \\ & V = \left\{ \frac{23}{12} \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{+12}& = & -13 \color{red}{ -9x } \\\Leftrightarrow & x \color{red}{+12}\color{blue}{-12+9x } & = & -13 \color{red}{ -9x }\color{blue}{-12+9x } \\\Leftrightarrow & x \color{blue}{+9x } & = & -13 \color{blue}{-12} \\\Leftrightarrow &10x & = &-25\\\Leftrightarrow & \color{red}{10}x & = &-25\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-25}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{-3}& = & -14 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{-3}\color{blue}{+3-14x } & = & -14 \color{red}{ +14x }\color{blue}{+3-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & -14 \color{blue}{+3} \\\Leftrightarrow &-25x & = &-11\\\Leftrightarrow & \color{red}{-25}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-11}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{11}{25} } & & \\ & V = \left\{ \frac{11}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{-5}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-5}\color{blue}{+5-x } & = & 3 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 3 \color{blue}{+5} \\\Leftrightarrow &-5x & = &8\\\Leftrightarrow & \color{red}{-5}x & = &8\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{8}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{-6}& = & -15 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{-6}\color{blue}{+6+4x } & = & -15 \color{red}{ -4x }\color{blue}{+6+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -15 \color{blue}{+6} \\\Leftrightarrow &13x & = &-9\\\Leftrightarrow & \color{red}{13}x & = &-9\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-9}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{13} } & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{-14}& = & 2 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-14}\color{blue}{+14-9x } & = & 2 \color{red}{ +9x }\color{blue}{+14-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & 2 \color{blue}{+14} \\\Leftrightarrow &-13x & = &16\\\Leftrightarrow & \color{red}{-13}x & = &16\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{16}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{13} } & & \\ & V = \left\{ \frac{-16}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{-7}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-7}\color{blue}{+7-x } & = & -2 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -2 \color{blue}{+7} \\\Leftrightarrow &-11x & = &5\\\Leftrightarrow & \color{red}{-11}x & = &5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{+8}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+8}\color{blue}{-8-x } & = & 1 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 1 \color{blue}{-8} \\\Leftrightarrow &-13x & = &-7\\\Leftrightarrow & \color{red}{-13}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{+4}& = & -5 \color{red}{ +3x } \\\Leftrightarrow & -14x \color{red}{+4}\color{blue}{-4-3x } & = & -5 \color{red}{ +3x }\color{blue}{-4-3x } \\\Leftrightarrow & -14x \color{blue}{-3x } & = & -5 \color{blue}{-4} \\\Leftrightarrow &-17x & = &-9\\\Leftrightarrow & \color{red}{-17}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-9}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{9}{17} } & & \\ & V = \left\{ \frac{9}{17} \right\} & \\\end{align}\)