Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{-3}& = & 1 \color{red}{ +2x } \\\Leftrightarrow & 9x \color{red}{-3}\color{blue}{+3-2x } & = & 1 \color{red}{ +2x }\color{blue}{+3-2x } \\\Leftrightarrow & 9x \color{blue}{-2x } & = & 1 \color{blue}{+3} \\\Leftrightarrow &7x & = &4\\\Leftrightarrow & \color{red}{7}x & = &4\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{4}{7} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{+1}& = & 13 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+1}\color{blue}{-1-5x } & = & 13 \color{red}{ +5x }\color{blue}{-1-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & 13 \color{blue}{-1} \\\Leftrightarrow &-14x & = &12\\\Leftrightarrow & \color{red}{-14}x & = &12\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{12}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{-5}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-5}\color{blue}{+5-x } & = & -13 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -13 \color{blue}{+5} \\\Leftrightarrow &5x & = &-8\\\Leftrightarrow & \color{red}{5}x & = &-8\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-8}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{-13}& = & -5 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{-13}\color{blue}{+13-14x } & = & -5 \color{red}{ +14x }\color{blue}{+13-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -5 \color{blue}{+13} \\\Leftrightarrow &-23x & = &8\\\Leftrightarrow & \color{red}{-23}x & = &8\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{8}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{23} } & & \\ & V = \left\{ \frac{-8}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{+13}& = & 14 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{+13}\color{blue}{-13+11x } & = & 14 \color{red}{ -11x }\color{blue}{-13+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & 14 \color{blue}{-13} \\\Leftrightarrow &26x & = &1\\\Leftrightarrow & \color{red}{26}x & = &1\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{1}{26} \\\Leftrightarrow & \color{green}{ x = \frac{1}{26} } & & \\ & V = \left\{ \frac{1}{26} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{+9}& = & -9 \color{red}{ +13x } \\\Leftrightarrow & -5x \color{red}{+9}\color{blue}{-9-13x } & = & -9 \color{red}{ +13x }\color{blue}{-9-13x } \\\Leftrightarrow & -5x \color{blue}{-13x } & = & -9 \color{blue}{-9} \\\Leftrightarrow &-18x & = &-18\\\Leftrightarrow & \color{red}{-18}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{-18}{-18} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{-14}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-14}\color{blue}{+14-x } & = & -10 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -10 \color{blue}{+14} \\\Leftrightarrow &-8x & = &4\\\Leftrightarrow & \color{red}{-8}x & = &4\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{4}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{-2}& = & 9 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{-2}\color{blue}{+2-8x } & = & 9 \color{red}{ +8x }\color{blue}{+2-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & 9 \color{blue}{+2} \\\Leftrightarrow &-15x & = &11\\\Leftrightarrow & \color{red}{-15}x & = &11\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{11}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{15} } & & \\ & V = \left\{ \frac{-11}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{+9}& = & -13 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{+9}\color{blue}{-9-4x } & = & -13 \color{red}{ +4x }\color{blue}{-9-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & -13 \color{blue}{-9} \\\Leftrightarrow &-19x & = &-22\\\Leftrightarrow & \color{red}{-19}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-22}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{22}{19} } & & \\ & V = \left\{ \frac{22}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{-5}& = & -12 \color{red}{ -9x } \\\Leftrightarrow & 14x \color{red}{-5}\color{blue}{+5+9x } & = & -12 \color{red}{ -9x }\color{blue}{+5+9x } \\\Leftrightarrow & 14x \color{blue}{+9x } & = & -12 \color{blue}{+5} \\\Leftrightarrow &23x & = &-7\\\Leftrightarrow & \color{red}{23}x & = &-7\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-7}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{23} } & & \\ & V = \left\{ \frac{-7}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{+3}& = & -4 \color{red}{ +7x } \\\Leftrightarrow & 6x \color{red}{+3}\color{blue}{-3-7x } & = & -4 \color{red}{ +7x }\color{blue}{-3-7x } \\\Leftrightarrow & 6x \color{blue}{-7x } & = & -4 \color{blue}{-3} \\\Leftrightarrow &-x & = &-7\\\Leftrightarrow & \color{red}{-}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-7}{-1} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{+4}& = & -10 \color{red}{ +4x } \\\Leftrightarrow & 15x \color{red}{+4}\color{blue}{-4-4x } & = & -10 \color{red}{ +4x }\color{blue}{-4-4x } \\\Leftrightarrow & 15x \color{blue}{-4x } & = & -10 \color{blue}{-4} \\\Leftrightarrow &11x & = &-14\\\Leftrightarrow & \color{red}{11}x & = &-14\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-14}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{11} } & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)