Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{+5}& = & 3 \color{red}{ +10x } \\\Leftrightarrow & 3x \color{red}{+5}\color{blue}{-5-10x } & = & 3 \color{red}{ +10x }\color{blue}{-5-10x } \\\Leftrightarrow & 3x \color{blue}{-10x } & = & 3 \color{blue}{-5} \\\Leftrightarrow &-7x & = &-2\\\Leftrightarrow & \color{red}{-7}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{+3}& = & -10 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{+3}\color{blue}{-3-8x } & = & -10 \color{red}{ +8x }\color{blue}{-3-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & -10 \color{blue}{-3} \\\Leftrightarrow &-15x & = &-13\\\Leftrightarrow & \color{red}{-15}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-13}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{13}{15} } & & \\ & V = \left\{ \frac{13}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{+3}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+3}\color{blue}{-3-x } & = & 2 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 2 \color{blue}{-3} \\\Leftrightarrow &-7x & = &-1\\\Leftrightarrow & \color{red}{-7}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{+12}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+12}\color{blue}{-12-x } & = & -7 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -7 \color{blue}{-12} \\\Leftrightarrow &-11x & = &-19\\\Leftrightarrow & \color{red}{-11}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-19}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{19}{11} } & & \\ & V = \left\{ \frac{19}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{-12}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-12}\color{blue}{+12-x } & = & -14 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -14 \color{blue}{+12} \\\Leftrightarrow &-15x & = &-2\\\Leftrightarrow & \color{red}{-15}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-2}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{15} } & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{-3}& = & -5 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{-3}\color{blue}{+3-7x } & = & -5 \color{red}{ +7x }\color{blue}{+3-7x } \\\Leftrightarrow & 12x \color{blue}{-7x } & = & -5 \color{blue}{+3} \\\Leftrightarrow &5x & = &-2\\\Leftrightarrow & \color{red}{5}x & = &-2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{-8}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-8}\color{blue}{+8-x } & = & 2 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 2 \color{blue}{+8} \\\Leftrightarrow &-10x & = &10\\\Leftrightarrow & \color{red}{-10}x & = &10\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{10}{-10} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{-10}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-10}\color{blue}{+10-x } & = & 7 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 7 \color{blue}{+10} \\\Leftrightarrow &-12x & = &17\\\Leftrightarrow & \color{red}{-12}x & = &17\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{17}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{12} } & & \\ & V = \left\{ \frac{-17}{12} \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{-1}& = & 12 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-1}\color{blue}{+1-13x } & = & 12 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 12 \color{blue}{+1} \\\Leftrightarrow &-25x & = &13\\\Leftrightarrow & \color{red}{-25}x & = &13\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{13}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{25} } & & \\ & V = \left\{ \frac{-13}{25} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{-8}& = & -7 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8+11x } & = & -7 \color{red}{ -11x }\color{blue}{+8+11x } \\\Leftrightarrow & 14x \color{blue}{+11x } & = & -7 \color{blue}{+8} \\\Leftrightarrow &25x & = &1\\\Leftrightarrow & \color{red}{25}x & = &1\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{1}{25} \\\Leftrightarrow & \color{green}{ x = \frac{1}{25} } & & \\ & V = \left\{ \frac{1}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{-6}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-6}\color{blue}{+6-7x } & = & -7 \color{red}{ +7x }\color{blue}{+6-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & -7 \color{blue}{+6} \\\Leftrightarrow &3x & = &-1\\\Leftrightarrow & \color{red}{3}x & = &-1\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-1}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{-12}& = & -7 \color{red}{ +3x } \\\Leftrightarrow & -x \color{red}{-12}\color{blue}{+12-3x } & = & -7 \color{red}{ +3x }\color{blue}{+12-3x } \\\Leftrightarrow & -x \color{blue}{-3x } & = & -7 \color{blue}{+12} \\\Leftrightarrow &-4x & = &5\\\Leftrightarrow & \color{red}{-4}x & = &5\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{5}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)