Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{+1}& = & -11 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+1}\color{blue}{-1+7x } & = & -11 \color{red}{ -7x }\color{blue}{-1+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & -11 \color{blue}{-1} \\\Leftrightarrow &11x & = &-12\\\Leftrightarrow & \color{red}{11}x & = &-12\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-12}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{11} } & & \\ & V = \left\{ \frac{-12}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{-1}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -x \color{red}{-1}\color{blue}{+1-x } & = & 8 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -x \color{blue}{-x } & = & 8 \color{blue}{+1} \\\Leftrightarrow &-2x & = &9\\\Leftrightarrow & \color{red}{-2}x & = &9\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{9}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{2} } & & \\ & V = \left\{ \frac{-9}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{+2}& = & -14 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{+2}\color{blue}{-2+4x } & = & -14 \color{red}{ -4x }\color{blue}{-2+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -14 \color{blue}{-2} \\\Leftrightarrow &13x & = &-16\\\Leftrightarrow & \color{red}{13}x & = &-16\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-16}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{13} } & & \\ & V = \left\{ \frac{-16}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{-15}& = & -5 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{-15}\color{blue}{+15-14x } & = & -5 \color{red}{ +14x }\color{blue}{+15-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & -5 \color{blue}{+15} \\\Leftrightarrow &-25x & = &10\\\Leftrightarrow & \color{red}{-25}x & = &10\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{10}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{+13}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{+13}\color{blue}{-13-x } & = & -14 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & -14 \color{blue}{-13} \\\Leftrightarrow &8x & = &-27\\\Leftrightarrow & \color{red}{8}x & = &-27\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-27}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{8} } & & \\ & V = \left\{ \frac{-27}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{+7}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+7}\color{blue}{-7-x } & = & -4 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -4 \color{blue}{-7} \\\Leftrightarrow &11x & = &-11\\\Leftrightarrow & \color{red}{11}x & = &-11\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-11}{11} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{-2}& = & -11 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{-2}\color{blue}{+2-5x } & = & -11 \color{red}{ +5x }\color{blue}{+2-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & -11 \color{blue}{+2} \\\Leftrightarrow &-14x & = &-9\\\Leftrightarrow & \color{red}{-14}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-9}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{9}{14} } & & \\ & V = \left\{ \frac{9}{14} \right\} & \\\end{align}\)
8. \(\begin{align} & -8x \color{red}{-2}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-2}\color{blue}{+2-x } & = & -14 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -14 \color{blue}{+2} \\\Leftrightarrow &-9x & = &-12\\\Leftrightarrow & \color{red}{-9}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-12}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{+12}& = & -12 \color{red}{ -9x } \\\Leftrightarrow & 14x \color{red}{+12}\color{blue}{-12+9x } & = & -12 \color{red}{ -9x }\color{blue}{-12+9x } \\\Leftrightarrow & 14x \color{blue}{+9x } & = & -12 \color{blue}{-12} \\\Leftrightarrow &23x & = &-24\\\Leftrightarrow & \color{red}{23}x & = &-24\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-24}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{23} } & & \\ & V = \left\{ \frac{-24}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{-8}& = & -9 \color{red}{ +7x } \\\Leftrightarrow & -x \color{red}{-8}\color{blue}{+8-7x } & = & -9 \color{red}{ +7x }\color{blue}{+8-7x } \\\Leftrightarrow & -x \color{blue}{-7x } & = & -9 \color{blue}{+8} \\\Leftrightarrow &-8x & = &-1\\\Leftrightarrow & \color{red}{-8}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{-15}& = & -11 \color{red}{ +3x } \\\Leftrightarrow & -11x \color{red}{-15}\color{blue}{+15-3x } & = & -11 \color{red}{ +3x }\color{blue}{+15-3x } \\\Leftrightarrow & -11x \color{blue}{-3x } & = & -11 \color{blue}{+15} \\\Leftrightarrow &-14x & = &4\\\Leftrightarrow & \color{red}{-14}x & = &4\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{4}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{+12}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+12}\color{blue}{-12-x } & = & 3 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 3 \color{blue}{-12} \\\Leftrightarrow &-14x & = &-9\\\Leftrightarrow & \color{red}{-14}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-9}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{9}{14} } & & \\ & V = \left\{ \frac{9}{14} \right\} & \\\end{align}\)