Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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