Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{-5}& = & -9 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-5}\color{blue}{+5-13x } & = & -9 \color{red}{ +13x }\color{blue}{+5-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -9 \color{blue}{+5} \\\Leftrightarrow &-25x & = &-4\\\Leftrightarrow & \color{red}{-25}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-4}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{4}{25} } & & \\ & V = \left\{ \frac{4}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{-4}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-4}\color{blue}{+4-x } & = & 11 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 11 \color{blue}{+4} \\\Leftrightarrow &-12x & = &15\\\Leftrightarrow & \color{red}{-12}x & = &15\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{15}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{-6}& = & -8 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{-6}\color{blue}{+6+3x } & = & -8 \color{red}{ -3x }\color{blue}{+6+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & -8 \color{blue}{+6} \\\Leftrightarrow &7x & = &-2\\\Leftrightarrow & \color{red}{7}x & = &-2\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-2}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{+1}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+1}\color{blue}{-1-x } & = & 10 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 10 \color{blue}{-1} \\\Leftrightarrow &-5x & = &9\\\Leftrightarrow & \color{red}{-5}x & = &9\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{9}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{-6}& = & 2 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-6}\color{blue}{+6+13x } & = & 2 \color{red}{ -13x }\color{blue}{+6+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & 2 \color{blue}{+6} \\\Leftrightarrow &23x & = &8\\\Leftrightarrow & \color{red}{23}x & = &8\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{8}{23} \\\Leftrightarrow & \color{green}{ x = \frac{8}{23} } & & \\ & V = \left\{ \frac{8}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{-14}& = & 11 \color{red}{ -2x } \\\Leftrightarrow & 5x \color{red}{-14}\color{blue}{+14+2x } & = & 11 \color{red}{ -2x }\color{blue}{+14+2x } \\\Leftrightarrow & 5x \color{blue}{+2x } & = & 11 \color{blue}{+14} \\\Leftrightarrow &7x & = &25\\\Leftrightarrow & \color{red}{7}x & = &25\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{25}{7} \\\Leftrightarrow & \color{green}{ x = \frac{25}{7} } & & \\ & V = \left\{ \frac{25}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{+13}& = & -9 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{+13}\color{blue}{-13-11x } & = & -9 \color{red}{ +11x }\color{blue}{-13-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & -9 \color{blue}{-13} \\\Leftrightarrow &4x & = &-22\\\Leftrightarrow & \color{red}{4}x & = &-22\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-22}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{2} } & & \\ & V = \left\{ \frac{-11}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{+5}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+5}\color{blue}{-5-x } & = & 6 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 6 \color{blue}{-5} \\\Leftrightarrow &-10x & = &1\\\Leftrightarrow & \color{red}{-10}x & = &1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{-9}& = & -11 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{-9}\color{blue}{+9-13x } & = & -11 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & -11 \color{blue}{+9} \\\Leftrightarrow &-17x & = &-2\\\Leftrightarrow & \color{red}{-17}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-2}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{2}{17} } & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{+9}& = & -14 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+9}\color{blue}{-9+7x } & = & -14 \color{red}{ -7x }\color{blue}{-9+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -14 \color{blue}{-9} \\\Leftrightarrow &15x & = &-23\\\Leftrightarrow & \color{red}{15}x & = &-23\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-23}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{15} } & & \\ & V = \left\{ \frac{-23}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{-10}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-10}\color{blue}{+10-x } & = & -15 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & -15 \color{blue}{+10} \\\Leftrightarrow &3x & = &-5\\\Leftrightarrow & \color{red}{3}x & = &-5\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-5}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{+2}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+2}\color{blue}{-2-x } & = & -3 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -3 \color{blue}{-2} \\\Leftrightarrow &x & = &-5\\\Leftrightarrow & \color{red}{}x & = &-5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -5 \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)