Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{-9}& = & -15 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{-9}\color{blue}{+9+15x } & = & -15 \color{red}{ -15x }\color{blue}{+9+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & -15 \color{blue}{+9} \\\Leftrightarrow &19x & = &-6\\\Leftrightarrow & \color{red}{19}x & = &-6\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-6}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{19} } & & \\ & V = \left\{ \frac{-6}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{-2}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-2}\color{blue}{+2-x } & = & -1 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -1 \color{blue}{+2} \\\Leftrightarrow &-9x & = &1\\\Leftrightarrow & \color{red}{-9}x & = &1\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{1}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{9} } & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{-14}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-14}\color{blue}{+14-x } & = & 11 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 11 \color{blue}{+14} \\\Leftrightarrow &-7x & = &25\\\Leftrightarrow & \color{red}{-7}x & = &25\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{25}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{7} } & & \\ & V = \left\{ \frac{-25}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{-10}& = & -8 \color{red}{ +8x } \\\Leftrightarrow & 15x \color{red}{-10}\color{blue}{+10-8x } & = & -8 \color{red}{ +8x }\color{blue}{+10-8x } \\\Leftrightarrow & 15x \color{blue}{-8x } & = & -8 \color{blue}{+10} \\\Leftrightarrow &7x & = &2\\\Leftrightarrow & \color{red}{7}x & = &2\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{2}{7} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{-12}& = & 13 \color{red}{ +5x } \\\Leftrightarrow & -7x \color{red}{-12}\color{blue}{+12-5x } & = & 13 \color{red}{ +5x }\color{blue}{+12-5x } \\\Leftrightarrow & -7x \color{blue}{-5x } & = & 13 \color{blue}{+12} \\\Leftrightarrow &-12x & = &25\\\Leftrightarrow & \color{red}{-12}x & = &25\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{25}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{12} } & & \\ & V = \left\{ \frac{-25}{12} \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{-13}& = & -13 \color{red}{ -15x } \\\Leftrightarrow & -x \color{red}{-13}\color{blue}{+13+15x } & = & -13 \color{red}{ -15x }\color{blue}{+13+15x } \\\Leftrightarrow & -x \color{blue}{+15x } & = & -13 \color{blue}{+13} \\\Leftrightarrow &14x & = &0\\\Leftrightarrow & \color{red}{14}x & = &0\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{0}{14} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{-9}& = & -5 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{-9}\color{blue}{+9-7x } & = & -5 \color{red}{ +7x }\color{blue}{+9-7x } \\\Leftrightarrow & -3x \color{blue}{-7x } & = & -5 \color{blue}{+9} \\\Leftrightarrow &-10x & = &4\\\Leftrightarrow & \color{red}{-10}x & = &4\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{4}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{-8}& = & 15 \color{red}{ +8x } \\\Leftrightarrow & 7x \color{red}{-8}\color{blue}{+8-8x } & = & 15 \color{red}{ +8x }\color{blue}{+8-8x } \\\Leftrightarrow & 7x \color{blue}{-8x } & = & 15 \color{blue}{+8} \\\Leftrightarrow &-x & = &23\\\Leftrightarrow & \color{red}{-}x & = &23\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{23}{-1} \\\Leftrightarrow & \color{green}{ x = -23 } & & \\ & V = \left\{ -23 \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{-6}& = & -4 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{-6}\color{blue}{+6-5x } & = & -4 \color{red}{ +5x }\color{blue}{+6-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & -4 \color{blue}{+6} \\\Leftrightarrow &x & = &2\\\Leftrightarrow & \color{red}{}x & = &2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 2 \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
10. \(\begin{align} & 15x \color{red}{+2}& = & 10 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{+2}\color{blue}{-2+11x } & = & 10 \color{red}{ -11x }\color{blue}{-2+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & 10 \color{blue}{-2} \\\Leftrightarrow &26x & = &8\\\Leftrightarrow & \color{red}{26}x & = &8\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{8}{26} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{-1}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-1}\color{blue}{+1-x } & = & 15 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 15 \color{blue}{+1} \\\Leftrightarrow &-11x & = &16\\\Leftrightarrow & \color{red}{-11}x & = &16\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{16}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{11} } & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{-5}& = & -1 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{-5}\color{blue}{+5+5x } & = & -1 \color{red}{ -5x }\color{blue}{+5+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & -1 \color{blue}{+5} \\\Leftrightarrow &11x & = &4\\\Leftrightarrow & \color{red}{11}x & = &4\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{4}{11} \\\Leftrightarrow & \color{green}{ x = \frac{4}{11} } & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)