Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 7x \color{red}{+9}& = & -1 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{+9}\color{blue}{-9+3x } & = & -1 \color{red}{ -3x }\color{blue}{-9+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & -1 \color{blue}{-9} \\\Leftrightarrow &10x & = &-10\\\Leftrightarrow & \color{red}{10}x & = &-10\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-10}{10} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{+10}& = & -10 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{+10}\color{blue}{-10-11x } & = & -10 \color{red}{ +11x }\color{blue}{-10-11x } \\\Leftrightarrow & 8x \color{blue}{-11x } & = & -10 \color{blue}{-10} \\\Leftrightarrow &-3x & = &-20\\\Leftrightarrow & \color{red}{-3}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-20}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{20}{3} } & & \\ & V = \left\{ \frac{20}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{-12}& = & 15 \color{red}{ -7x } \\\Leftrightarrow & 5x \color{red}{-12}\color{blue}{+12+7x } & = & 15 \color{red}{ -7x }\color{blue}{+12+7x } \\\Leftrightarrow & 5x \color{blue}{+7x } & = & 15 \color{blue}{+12} \\\Leftrightarrow &12x & = &27\\\Leftrightarrow & \color{red}{12}x & = &27\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{27}{12} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -8x \color{red}{-1}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-1}\color{blue}{+1-x } & = & -15 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -15 \color{blue}{+1} \\\Leftrightarrow &-9x & = &-14\\\Leftrightarrow & \color{red}{-9}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-14}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{14}{9} } & & \\ & V = \left\{ \frac{14}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+13}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+13}\color{blue}{-13-x } & = & -3 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -3 \color{blue}{-13} \\\Leftrightarrow &-9x & = &-16\\\Leftrightarrow & \color{red}{-9}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-16}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{16}{9} } & & \\ & V = \left\{ \frac{16}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{+10}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+10}\color{blue}{-10-x } & = & -11 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & -11 \color{blue}{-10} \\\Leftrightarrow &9x & = &-21\\\Leftrightarrow & \color{red}{9}x & = &-21\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-21}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{+8}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+8}\color{blue}{-8-x } & = & 12 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 12 \color{blue}{-8} \\\Leftrightarrow &-8x & = &4\\\Leftrightarrow & \color{red}{-8}x & = &4\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{4}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{+10}& = & 15 \color{red}{ -4x } \\\Leftrightarrow & -x \color{red}{+10}\color{blue}{-10+4x } & = & 15 \color{red}{ -4x }\color{blue}{-10+4x } \\\Leftrightarrow & -x \color{blue}{+4x } & = & 15 \color{blue}{-10} \\\Leftrightarrow &3x & = &5\\\Leftrightarrow & \color{red}{3}x & = &5\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{5}{3} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{-6}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-6}\color{blue}{+6-x } & = & 12 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 12 \color{blue}{+6} \\\Leftrightarrow &-4x & = &18\\\Leftrightarrow & \color{red}{-4}x & = &18\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{18}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{2} } & & \\ & V = \left\{ \frac{-9}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{-12}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-12}\color{blue}{+12-x } & = & -12 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -12 \color{blue}{+12} \\\Leftrightarrow &-6x & = &0\\\Leftrightarrow & \color{red}{-6}x & = &0\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{0}{-6} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{-1}& = & -1 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{-1}\color{blue}{+1+10x } & = & -1 \color{red}{ -10x }\color{blue}{+1+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & -1 \color{blue}{+1} \\\Leftrightarrow &17x & = &0\\\Leftrightarrow & \color{red}{17}x & = &0\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{0}{17} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{+8}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+8}\color{blue}{-8-x } & = & -10 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -10 \color{blue}{-8} \\\Leftrightarrow &-8x & = &-18\\\Leftrightarrow & \color{red}{-8}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-18}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)