Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{-3}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-3}\color{blue}{+3-x } & = & -5 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -5 \color{blue}{+3} \\\Leftrightarrow &-7x & = &-2\\\Leftrightarrow & \color{red}{-7}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{+2}& = & -3 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{+2}\color{blue}{-2-13x } & = & -3 \color{red}{ +13x }\color{blue}{-2-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & -3 \color{blue}{-2} \\\Leftrightarrow &-3x & = &-5\\\Leftrightarrow & \color{red}{-3}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-5}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{-3}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-3}\color{blue}{+3-x } & = & 5 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 5 \color{blue}{+3} \\\Leftrightarrow &-9x & = &8\\\Leftrightarrow & \color{red}{-9}x & = &8\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{8}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{9} } & & \\ & V = \left\{ \frac{-8}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{-5}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{-5}\color{blue}{+5-x } & = & 7 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & 7 \color{blue}{+5} \\\Leftrightarrow &2x & = &12\\\Leftrightarrow & \color{red}{2}x & = &12\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{12}{2} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{+15}& = & -14 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+15}\color{blue}{-15-13x } & = & -14 \color{red}{ +13x }\color{blue}{-15-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -14 \color{blue}{-15} \\\Leftrightarrow &-28x & = &-29\\\Leftrightarrow & \color{red}{-28}x & = &-29\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-29}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{29}{28} } & & \\ & V = \left\{ \frac{29}{28} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{+3}& = & -12 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+3}\color{blue}{-3+7x } & = & -12 \color{red}{ -7x }\color{blue}{-3+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -12 \color{blue}{-3} \\\Leftrightarrow &15x & = &-15\\\Leftrightarrow & \color{red}{15}x & = &-15\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-15}{15} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{+7}& = & -12 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+7}\color{blue}{-7+13x } & = & -12 \color{red}{ -13x }\color{blue}{-7+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & -12 \color{blue}{-7} \\\Leftrightarrow &24x & = &-19\\\Leftrightarrow & \color{red}{24}x & = &-19\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-19}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{24} } & & \\ & V = \left\{ \frac{-19}{24} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{-8}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-8}\color{blue}{+8-x } & = & -15 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -15 \color{blue}{+8} \\\Leftrightarrow &-3x & = &-7\\\Leftrightarrow & \color{red}{-3}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-7}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{-15}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-15}\color{blue}{+15-x } & = & 8 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 8 \color{blue}{+15} \\\Leftrightarrow &-9x & = &23\\\Leftrightarrow & \color{red}{-9}x & = &23\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{23}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{9} } & & \\ & V = \left\{ \frac{-23}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{+6}& = & -8 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{+6}\color{blue}{-6+9x } & = & -8 \color{red}{ -9x }\color{blue}{-6+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & -8 \color{blue}{-6} \\\Leftrightarrow &14x & = &-14\\\Leftrightarrow & \color{red}{14}x & = &-14\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-14}{14} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{-14}& = & -13 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{-14}\color{blue}{+14+3x } & = & -13 \color{red}{ -3x }\color{blue}{+14+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & -13 \color{blue}{+14} \\\Leftrightarrow &10x & = &1\\\Leftrightarrow & \color{red}{10}x & = &1\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{1}{10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{10} } & & \\ & V = \left\{ \frac{1}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{+11}& = & -13 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{+11}\color{blue}{-11+14x } & = & -13 \color{red}{ -14x }\color{blue}{-11+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & -13 \color{blue}{-11} \\\Leftrightarrow &29x & = &-24\\\Leftrightarrow & \color{red}{29}x & = &-24\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{-24}{29} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{29} } & & \\ & V = \left\{ \frac{-24}{29} \right\} & \\\end{align}\)