Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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