Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{-11}& = & -4 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-11}\color{blue}{+11-7x } & = & -4 \color{red}{ +7x }\color{blue}{+11-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -4 \color{blue}{+11} \\\Leftrightarrow &-17x & = &7\\\Leftrightarrow & \color{red}{-17}x & = &7\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{7}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{17} } & & \\ & V = \left\{ \frac{-7}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{+7}& = & 2 \color{red}{ -12x } \\\Leftrightarrow & -13x \color{red}{+7}\color{blue}{-7+12x } & = & 2 \color{red}{ -12x }\color{blue}{-7+12x } \\\Leftrightarrow & -13x \color{blue}{+12x } & = & 2 \color{blue}{-7} \\\Leftrightarrow &-x & = &-5\\\Leftrightarrow & \color{red}{-}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-5}{-1} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{+15}& = & -4 \color{red}{ +14x } \\\Leftrightarrow & 11x \color{red}{+15}\color{blue}{-15-14x } & = & -4 \color{red}{ +14x }\color{blue}{-15-14x } \\\Leftrightarrow & 11x \color{blue}{-14x } & = & -4 \color{blue}{-15} \\\Leftrightarrow &-3x & = &-19\\\Leftrightarrow & \color{red}{-3}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-19}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{19}{3} } & & \\ & V = \left\{ \frac{19}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{+5}& = & 3 \color{red}{ +11x } \\\Leftrightarrow & -x \color{red}{+5}\color{blue}{-5-11x } & = & 3 \color{red}{ +11x }\color{blue}{-5-11x } \\\Leftrightarrow & -x \color{blue}{-11x } & = & 3 \color{blue}{-5} \\\Leftrightarrow &-12x & = &-2\\\Leftrightarrow & \color{red}{-12}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-2}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{+8}& = & 1 \color{red}{ +5x } \\\Leftrightarrow & 3x \color{red}{+8}\color{blue}{-8-5x } & = & 1 \color{red}{ +5x }\color{blue}{-8-5x } \\\Leftrightarrow & 3x \color{blue}{-5x } & = & 1 \color{blue}{-8} \\\Leftrightarrow &-2x & = &-7\\\Leftrightarrow & \color{red}{-2}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-7}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{-13}& = & -5 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{-13}\color{blue}{+13-7x } & = & -5 \color{red}{ +7x }\color{blue}{+13-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & -5 \color{blue}{+13} \\\Leftrightarrow &-5x & = &8\\\Leftrightarrow & \color{red}{-5}x & = &8\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{8}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{+7}& = & -3 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{+7}\color{blue}{-7-10x } & = & -3 \color{red}{ +10x }\color{blue}{-7-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & -3 \color{blue}{-7} \\\Leftrightarrow &-19x & = &-10\\\Leftrightarrow & \color{red}{-19}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-10}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{10}{19} } & & \\ & V = \left\{ \frac{10}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{-11}& = & -1 \color{red}{ +9x } \\\Leftrightarrow & -13x \color{red}{-11}\color{blue}{+11-9x } & = & -1 \color{red}{ +9x }\color{blue}{+11-9x } \\\Leftrightarrow & -13x \color{blue}{-9x } & = & -1 \color{blue}{+11} \\\Leftrightarrow &-22x & = &10\\\Leftrightarrow & \color{red}{-22}x & = &10\\\Leftrightarrow & \frac{\color{red}{-22}x}{ \color{blue}{ -22}} & = & \frac{10}{-22} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{-7}& = & -12 \color{red}{ +7x } \\\Leftrightarrow & 6x \color{red}{-7}\color{blue}{+7-7x } & = & -12 \color{red}{ +7x }\color{blue}{+7-7x } \\\Leftrightarrow & 6x \color{blue}{-7x } & = & -12 \color{blue}{+7} \\\Leftrightarrow &-x & = &-5\\\Leftrightarrow & \color{red}{-}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-5}{-1} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{+3}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+3}\color{blue}{-3-x } & = & 2 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 2 \color{blue}{-3} \\\Leftrightarrow &-4x & = &-1\\\Leftrightarrow & \color{red}{-4}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{+11}& = & -11 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+11}\color{blue}{-11-14x } & = & -11 \color{red}{ +14x }\color{blue}{-11-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -11 \color{blue}{-11} \\\Leftrightarrow &-23x & = &-22\\\Leftrightarrow & \color{red}{-23}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-22}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{22}{23} } & & \\ & V = \left\{ \frac{22}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{-12}& = & 9 \color{red}{ +9x } \\\Leftrightarrow & 11x \color{red}{-12}\color{blue}{+12-9x } & = & 9 \color{red}{ +9x }\color{blue}{+12-9x } \\\Leftrightarrow & 11x \color{blue}{-9x } & = & 9 \color{blue}{+12} \\\Leftrightarrow &2x & = &21\\\Leftrightarrow & \color{red}{2}x & = &21\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{21}{2} \\\Leftrightarrow & \color{green}{ x = \frac{21}{2} } & & \\ & V = \left\{ \frac{21}{2} \right\} & \\\end{align}\)