Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{+1}& = & -9 \color{red}{ +11x } \\\Leftrightarrow & 9x \color{red}{+1}\color{blue}{-1-11x } & = & -9 \color{red}{ +11x }\color{blue}{-1-11x } \\\Leftrightarrow & 9x \color{blue}{-11x } & = & -9 \color{blue}{-1} \\\Leftrightarrow &-2x & = &-10\\\Leftrightarrow & \color{red}{-2}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-10}{-2} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{+2}& = & -2 \color{red}{ +3x } \\\Leftrightarrow & 14x \color{red}{+2}\color{blue}{-2-3x } & = & -2 \color{red}{ +3x }\color{blue}{-2-3x } \\\Leftrightarrow & 14x \color{blue}{-3x } & = & -2 \color{blue}{-2} \\\Leftrightarrow &11x & = &-4\\\Leftrightarrow & \color{red}{11}x & = &-4\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-4}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{+4}& = & -6 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{+4}\color{blue}{-4-5x } & = & -6 \color{red}{ +5x }\color{blue}{-4-5x } \\\Leftrightarrow & -2x \color{blue}{-5x } & = & -6 \color{blue}{-4} \\\Leftrightarrow &-7x & = &-10\\\Leftrightarrow & \color{red}{-7}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-10}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{10}{7} } & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{+6}& = & -14 \color{red}{ +9x } \\\Leftrightarrow & 2x \color{red}{+6}\color{blue}{-6-9x } & = & -14 \color{red}{ +9x }\color{blue}{-6-9x } \\\Leftrightarrow & 2x \color{blue}{-9x } & = & -14 \color{blue}{-6} \\\Leftrightarrow &-7x & = &-20\\\Leftrightarrow & \color{red}{-7}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-20}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{20}{7} } & & \\ & V = \left\{ \frac{20}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{-8}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8-x } & = & 4 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 4 \color{blue}{+8} \\\Leftrightarrow &13x & = &12\\\Leftrightarrow & \color{red}{13}x & = &12\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{12}{13} \\\Leftrightarrow & \color{green}{ x = \frac{12}{13} } & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{-12}& = & 1 \color{red}{ +8x } \\\Leftrightarrow & -5x \color{red}{-12}\color{blue}{+12-8x } & = & 1 \color{red}{ +8x }\color{blue}{+12-8x } \\\Leftrightarrow & -5x \color{blue}{-8x } & = & 1 \color{blue}{+12} \\\Leftrightarrow &-13x & = &13\\\Leftrightarrow & \color{red}{-13}x & = &13\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{13}{-13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{-6}& = & -11 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-6}\color{blue}{+6+8x } & = & -11 \color{red}{ -8x }\color{blue}{+6+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & -11 \color{blue}{+6} \\\Leftrightarrow &11x & = &-5\\\Leftrightarrow & \color{red}{11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{+4}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+4}\color{blue}{-4-x } & = & 5 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 5 \color{blue}{-4} \\\Leftrightarrow &-7x & = &1\\\Leftrightarrow & \color{red}{-7}x & = &1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -9x \color{red}{-3}& = & -5 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{-3}\color{blue}{+3-5x } & = & -5 \color{red}{ +5x }\color{blue}{+3-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & -5 \color{blue}{+3} \\\Leftrightarrow &-14x & = &-2\\\Leftrightarrow & \color{red}{-14}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-2}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{+7}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+7}\color{blue}{-7-x } & = & 15 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 15 \color{blue}{-7} \\\Leftrightarrow &-8x & = &8\\\Leftrightarrow & \color{red}{-8}x & = &8\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{8}{-8} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{-3}& = & 13 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{-3}\color{blue}{+3+12x } & = & 13 \color{red}{ -12x }\color{blue}{+3+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & 13 \color{blue}{+3} \\\Leftrightarrow &25x & = &16\\\Leftrightarrow & \color{red}{25}x & = &16\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{16}{25} \\\Leftrightarrow & \color{green}{ x = \frac{16}{25} } & & \\ & V = \left\{ \frac{16}{25} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{+8}& = & 11 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+8}\color{blue}{-8-5x } & = & 11 \color{red}{ +5x }\color{blue}{-8-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & 11 \color{blue}{-8} \\\Leftrightarrow &-14x & = &3\\\Leftrightarrow & \color{red}{-14}x & = &3\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{3}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{14} } & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)