Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{+6}& = & -8 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6+14x } & = & -8 \color{red}{ -14x }\color{blue}{-6+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & -8 \color{blue}{-6} \\\Leftrightarrow &29x & = &-14\\\Leftrightarrow & \color{red}{29}x & = &-14\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{-14}{29} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{29} } & & \\ & V = \left\{ \frac{-14}{29} \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{-11}& = & -5 \color{red}{ +11x } \\\Leftrightarrow & 5x \color{red}{-11}\color{blue}{+11-11x } & = & -5 \color{red}{ +11x }\color{blue}{+11-11x } \\\Leftrightarrow & 5x \color{blue}{-11x } & = & -5 \color{blue}{+11} \\\Leftrightarrow &-6x & = &6\\\Leftrightarrow & \color{red}{-6}x & = &6\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{6}{-6} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{-1}& = & 12 \color{red}{ +4x } \\\Leftrightarrow & 9x \color{red}{-1}\color{blue}{+1-4x } & = & 12 \color{red}{ +4x }\color{blue}{+1-4x } \\\Leftrightarrow & 9x \color{blue}{-4x } & = & 12 \color{blue}{+1} \\\Leftrightarrow &5x & = &13\\\Leftrightarrow & \color{red}{5}x & = &13\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{13}{5} \\\Leftrightarrow & \color{green}{ x = \frac{13}{5} } & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{+10}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{+10}\color{blue}{-10-x } & = & -6 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & -6 \color{blue}{-10} \\\Leftrightarrow &4x & = &-16\\\Leftrightarrow & \color{red}{4}x & = &-16\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-16}{4} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+3}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+3}\color{blue}{-3-x } & = & -4 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -4 \color{blue}{-3} \\\Leftrightarrow &-9x & = &-7\\\Leftrightarrow & \color{red}{-9}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{9} } & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{-15}& = & 11 \color{red}{ +4x } \\\Leftrightarrow & 15x \color{red}{-15}\color{blue}{+15-4x } & = & 11 \color{red}{ +4x }\color{blue}{+15-4x } \\\Leftrightarrow & 15x \color{blue}{-4x } & = & 11 \color{blue}{+15} \\\Leftrightarrow &11x & = &26\\\Leftrightarrow & \color{red}{11}x & = &26\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{26}{11} \\\Leftrightarrow & \color{green}{ x = \frac{26}{11} } & & \\ & V = \left\{ \frac{26}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{-6}& = & 8 \color{red}{ +6x } \\\Leftrightarrow & 5x \color{red}{-6}\color{blue}{+6-6x } & = & 8 \color{red}{ +6x }\color{blue}{+6-6x } \\\Leftrightarrow & 5x \color{blue}{-6x } & = & 8 \color{blue}{+6} \\\Leftrightarrow &-x & = &14\\\Leftrightarrow & \color{red}{-}x & = &14\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{14}{-1} \\\Leftrightarrow & \color{green}{ x = -14 } & & \\ & V = \left\{ -14 \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{-4}& = & 6 \color{red}{ +5x } \\\Leftrightarrow & x \color{red}{-4}\color{blue}{+4-5x } & = & 6 \color{red}{ +5x }\color{blue}{+4-5x } \\\Leftrightarrow & x \color{blue}{-5x } & = & 6 \color{blue}{+4} \\\Leftrightarrow &-4x & = &10\\\Leftrightarrow & \color{red}{-4}x & = &10\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{10}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{-5}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-5}\color{blue}{+5-x } & = & 14 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 14 \color{blue}{+5} \\\Leftrightarrow &-8x & = &19\\\Leftrightarrow & \color{red}{-8}x & = &19\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{19}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{8} } & & \\ & V = \left\{ \frac{-19}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{-4}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-4}\color{blue}{+4-x } & = & -3 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -3 \color{blue}{+4} \\\Leftrightarrow &-14x & = &1\\\Leftrightarrow & \color{red}{-14}x & = &1\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{1}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{14} } & & \\ & V = \left\{ \frac{-1}{14} \right\} & \\\end{align}\)
11. \(\begin{align} & 2x \color{red}{-11}& = & 10 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{-11}\color{blue}{+11-7x } & = & 10 \color{red}{ +7x }\color{blue}{+11-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & 10 \color{blue}{+11} \\\Leftrightarrow &-5x & = &21\\\Leftrightarrow & \color{red}{-5}x & = &21\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{21}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{5} } & & \\ & V = \left\{ \frac{-21}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{+11}& = & 7 \color{red}{ -14x } \\\Leftrightarrow & x \color{red}{+11}\color{blue}{-11+14x } & = & 7 \color{red}{ -14x }\color{blue}{-11+14x } \\\Leftrightarrow & x \color{blue}{+14x } & = & 7 \color{blue}{-11} \\\Leftrightarrow &15x & = &-4\\\Leftrightarrow & \color{red}{15}x & = &-4\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-4}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{15} } & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)