Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{-1}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-1}\color{blue}{+1-x } & = & 13 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & 13 \color{blue}{+1} \\\Leftrightarrow &9x & = &14\\\Leftrightarrow & \color{red}{9}x & = &14\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{14}{9} \\\Leftrightarrow & \color{green}{ x = \frac{14}{9} } & & \\ & V = \left\{ \frac{14}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{-6}& = & -10 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{-6}\color{blue}{+6+4x } & = & -10 \color{red}{ -4x }\color{blue}{+6+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -10 \color{blue}{+6} \\\Leftrightarrow &13x & = &-4\\\Leftrightarrow & \color{red}{13}x & = &-4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{-13}& = & -8 \color{red}{ +13x } \\\Leftrightarrow & 3x \color{red}{-13}\color{blue}{+13-13x } & = & -8 \color{red}{ +13x }\color{blue}{+13-13x } \\\Leftrightarrow & 3x \color{blue}{-13x } & = & -8 \color{blue}{+13} \\\Leftrightarrow &-10x & = &5\\\Leftrightarrow & \color{red}{-10}x & = &5\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{5}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{-13}& = & -6 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{-13}\color{blue}{+13-14x } & = & -6 \color{red}{ +14x }\color{blue}{+13-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -6 \color{blue}{+13} \\\Leftrightarrow &-23x & = &7\\\Leftrightarrow & \color{red}{-23}x & = &7\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{7}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{23} } & & \\ & V = \left\{ \frac{-7}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{-8}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-8}\color{blue}{+8-x } & = & -13 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -13 \color{blue}{+8} \\\Leftrightarrow &-13x & = &-5\\\Leftrightarrow & \color{red}{-13}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-5}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{5}{13} } & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{-12}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-12}\color{blue}{+12-x } & = & -7 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -7 \color{blue}{+12} \\\Leftrightarrow &-3x & = &5\\\Leftrightarrow & \color{red}{-3}x & = &5\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{5}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{-1}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-1}\color{blue}{+1-x } & = & 15 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 15 \color{blue}{+1} \\\Leftrightarrow &-11x & = &16\\\Leftrightarrow & \color{red}{-11}x & = &16\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{16}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{11} } & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{+9}& = & -2 \color{red}{ -2x } \\\Leftrightarrow & x \color{red}{+9}\color{blue}{-9+2x } & = & -2 \color{red}{ -2x }\color{blue}{-9+2x } \\\Leftrightarrow & x \color{blue}{+2x } & = & -2 \color{blue}{-9} \\\Leftrightarrow &3x & = &-11\\\Leftrightarrow & \color{red}{3}x & = &-11\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-11}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{-4}& = & -2 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-4}\color{blue}{+4+2x } & = & -2 \color{red}{ -2x }\color{blue}{+4+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -2 \color{blue}{+4} \\\Leftrightarrow &17x & = &2\\\Leftrightarrow & \color{red}{17}x & = &2\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{2}{17} \\\Leftrightarrow & \color{green}{ x = \frac{2}{17} } & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{-14}& = & -3 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{-14}\color{blue}{+14+12x } & = & -3 \color{red}{ -12x }\color{blue}{+14+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & -3 \color{blue}{+14} \\\Leftrightarrow &25x & = &11\\\Leftrightarrow & \color{red}{25}x & = &11\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{11}{25} \\\Leftrightarrow & \color{green}{ x = \frac{11}{25} } & & \\ & V = \left\{ \frac{11}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{-9}& = & -11 \color{red}{ +13x } \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9-13x } & = & -11 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & -5x \color{blue}{-13x } & = & -11 \color{blue}{+9} \\\Leftrightarrow &-18x & = &-2\\\Leftrightarrow & \color{red}{-18}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{-2}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & 3x \color{red}{-12}& = & -12 \color{red}{ -14x } \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12+14x } & = & -12 \color{red}{ -14x }\color{blue}{+12+14x } \\\Leftrightarrow & 3x \color{blue}{+14x } & = & -12 \color{blue}{+12} \\\Leftrightarrow &17x & = &0\\\Leftrightarrow & \color{red}{17}x & = &0\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{0}{17} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)