Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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