Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{+10}& = & 7 \color{red}{ +3x } \\\Leftrightarrow & 10x \color{red}{+10}\color{blue}{-10-3x } & = & 7 \color{red}{ +3x }\color{blue}{-10-3x } \\\Leftrightarrow & 10x \color{blue}{-3x } & = & 7 \color{blue}{-10} \\\Leftrightarrow &7x & = &-3\\\Leftrightarrow & \color{red}{7}x & = &-3\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-3}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{+13}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+13}\color{blue}{-13-x } & = & -12 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -12 \color{blue}{-13} \\\Leftrightarrow &-6x & = &-25\\\Leftrightarrow & \color{red}{-6}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-25}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{25}{6} } & & \\ & V = \left\{ \frac{25}{6} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{-6}& = & -15 \color{red}{ +8x } \\\Leftrightarrow & 5x \color{red}{-6}\color{blue}{+6-8x } & = & -15 \color{red}{ +8x }\color{blue}{+6-8x } \\\Leftrightarrow & 5x \color{blue}{-8x } & = & -15 \color{blue}{+6} \\\Leftrightarrow &-3x & = &-9\\\Leftrightarrow & \color{red}{-3}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-9}{-3} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{+6}& = & 6 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+6}\color{blue}{-6+7x } & = & 6 \color{red}{ -7x }\color{blue}{-6+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 6 \color{blue}{-6} \\\Leftrightarrow &15x & = &0\\\Leftrightarrow & \color{red}{15}x & = &0\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{0}{15} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{-1}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-1}\color{blue}{+1-x } & = & 12 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 12 \color{blue}{+1} \\\Leftrightarrow &-12x & = &13\\\Leftrightarrow & \color{red}{-12}x & = &13\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{13}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{12} } & & \\ & V = \left\{ \frac{-13}{12} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{-11}& = & -12 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11-11x } & = & -12 \color{red}{ +11x }\color{blue}{+11-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & -12 \color{blue}{+11} \\\Leftrightarrow &-16x & = &-1\\\Leftrightarrow & \color{red}{-16}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{16} } & & \\ & V = \left\{ \frac{1}{16} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{-9}& = & -8 \color{red}{ +8x } \\\Leftrightarrow & 7x \color{red}{-9}\color{blue}{+9-8x } & = & -8 \color{red}{ +8x }\color{blue}{+9-8x } \\\Leftrightarrow & 7x \color{blue}{-8x } & = & -8 \color{blue}{+9} \\\Leftrightarrow &-x & = &1\\\Leftrightarrow & \color{red}{-}x & = &1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{1}{-1} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+3}& = & -6 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+3}\color{blue}{-3-7x } & = & -6 \color{red}{ +7x }\color{blue}{-3-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -6 \color{blue}{-3} \\\Leftrightarrow &-17x & = &-9\\\Leftrightarrow & \color{red}{-17}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-9}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{9}{17} } & & \\ & V = \left\{ \frac{9}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{-7}& = & -9 \color{red}{ +7x } \\\Leftrightarrow & -2x \color{red}{-7}\color{blue}{+7-7x } & = & -9 \color{red}{ +7x }\color{blue}{+7-7x } \\\Leftrightarrow & -2x \color{blue}{-7x } & = & -9 \color{blue}{+7} \\\Leftrightarrow &-9x & = &-2\\\Leftrightarrow & \color{red}{-9}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{9} } & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{+4}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+4}\color{blue}{-4-x } & = & 3 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 3 \color{blue}{-4} \\\Leftrightarrow &x & = &-1\\\Leftrightarrow & \color{red}{}x & = &-1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -1 \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{-10}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{-10}\color{blue}{+10-13x } & = & 13 \color{red}{ +13x }\color{blue}{+10-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & 13 \color{blue}{+10} \\\Leftrightarrow &-17x & = &23\\\Leftrightarrow & \color{red}{-17}x & = &23\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{23}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{17} } & & \\ & V = \left\{ \frac{-23}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{-8}& = & 13 \color{red}{ +5x } \\\Leftrightarrow & 8x \color{red}{-8}\color{blue}{+8-5x } & = & 13 \color{red}{ +5x }\color{blue}{+8-5x } \\\Leftrightarrow & 8x \color{blue}{-5x } & = & 13 \color{blue}{+8} \\\Leftrightarrow &3x & = &21\\\Leftrightarrow & \color{red}{3}x & = &21\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{21}{3} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)