Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{+7}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{+7}\color{blue}{-7-13x } & = & 11 \color{red}{ +13x }\color{blue}{-7-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & 11 \color{blue}{-7} \\\Leftrightarrow &-3x & = &4\\\Leftrightarrow & \color{red}{-3}x & = &4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{+14}& = & 2 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{+14}\color{blue}{-14+11x } & = & 2 \color{red}{ -11x }\color{blue}{-14+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & 2 \color{blue}{-14} \\\Leftrightarrow &26x & = &-12\\\Leftrightarrow & \color{red}{26}x & = &-12\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{-12}{26} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{+2}& = & 1 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+2}\color{blue}{-2+13x } & = & 1 \color{red}{ -13x }\color{blue}{-2+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & 1 \color{blue}{-2} \\\Leftrightarrow &24x & = &-1\\\Leftrightarrow & \color{red}{24}x & = &-1\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-1}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{24} } & & \\ & V = \left\{ \frac{-1}{24} \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{+13}& = & -2 \color{red}{ -14x } \\\Leftrightarrow & -x \color{red}{+13}\color{blue}{-13+14x } & = & -2 \color{red}{ -14x }\color{blue}{-13+14x } \\\Leftrightarrow & -x \color{blue}{+14x } & = & -2 \color{blue}{-13} \\\Leftrightarrow &13x & = &-15\\\Leftrightarrow & \color{red}{13}x & = &-15\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-15}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{13} } & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{-2}& = & -5 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{-2}\color{blue}{+2-9x } & = & -5 \color{red}{ +9x }\color{blue}{+2-9x } \\\Leftrightarrow & 8x \color{blue}{-9x } & = & -5 \color{blue}{+2} \\\Leftrightarrow &-x & = &-3\\\Leftrightarrow & \color{red}{-}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-3}{-1} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{+8}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+8}\color{blue}{-8-x } & = & 2 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 2 \color{blue}{-8} \\\Leftrightarrow &-12x & = &-6\\\Leftrightarrow & \color{red}{-12}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-6}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{+10}& = & -14 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+10}\color{blue}{-10+13x } & = & -14 \color{red}{ -13x }\color{blue}{-10+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -14 \color{blue}{-10} \\\Leftrightarrow &27x & = &-24\\\Leftrightarrow & \color{red}{27}x & = &-24\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-24}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{9} } & & \\ & V = \left\{ \frac{-8}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{+12}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+12}\color{blue}{-12-x } & = & -8 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -8 \color{blue}{-12} \\\Leftrightarrow &-13x & = &-20\\\Leftrightarrow & \color{red}{-13}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-20}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{20}{13} } & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{-9}& = & -11 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{-9}\color{blue}{+9-6x } & = & -11 \color{red}{ +6x }\color{blue}{+9-6x } \\\Leftrightarrow & -11x \color{blue}{-6x } & = & -11 \color{blue}{+9} \\\Leftrightarrow &-17x & = &-2\\\Leftrightarrow & \color{red}{-17}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-2}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{2}{17} } & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{+1}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+1}\color{blue}{-1-x } & = & 14 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 14 \color{blue}{-1} \\\Leftrightarrow &-5x & = &13\\\Leftrightarrow & \color{red}{-5}x & = &13\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{13}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{5} } & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{+7}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+7}\color{blue}{-7-x } & = & -7 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -7 \color{blue}{-7} \\\Leftrightarrow &-12x & = &-14\\\Leftrightarrow & \color{red}{-12}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-14}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{6} } & & \\ & V = \left\{ \frac{7}{6} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{-10}& = & -8 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-10}\color{blue}{+10+7x } & = & -8 \color{red}{ -7x }\color{blue}{+10+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -8 \color{blue}{+10} \\\Leftrightarrow &15x & = &2\\\Leftrightarrow & \color{red}{15}x & = &2\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{2}{15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{15} } & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)