Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{-11}& = & 8 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{-11}\color{blue}{+11-11x } & = & 8 \color{red}{ +11x }\color{blue}{+11-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & 8 \color{blue}{+11} \\\Leftrightarrow &-9x & = &19\\\Leftrightarrow & \color{red}{-9}x & = &19\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{19}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{9} } & & \\ & V = \left\{ \frac{-19}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{-11}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 15x \color{red}{-11}\color{blue}{+11-x } & = & -6 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 15x \color{blue}{-x } & = & -6 \color{blue}{+11} \\\Leftrightarrow &14x & = &5\\\Leftrightarrow & \color{red}{14}x & = &5\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{5}{14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{14} } & & \\ & V = \left\{ \frac{5}{14} \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{+8}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+8}\color{blue}{-8-x } & = & -8 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -8 \color{blue}{-8} \\\Leftrightarrow &-5x & = &-16\\\Leftrightarrow & \color{red}{-5}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-16}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{16}{5} } & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{-11}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-11}\color{blue}{+11-x } & = & -10 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -10 \color{blue}{+11} \\\Leftrightarrow &-7x & = &1\\\Leftrightarrow & \color{red}{-7}x & = &1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{-1}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & 15x \color{red}{-1}\color{blue}{+1-13x } & = & 9 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & 15x \color{blue}{-13x } & = & 9 \color{blue}{+1} \\\Leftrightarrow &2x & = &10\\\Leftrightarrow & \color{red}{2}x & = &10\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{10}{2} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{-1}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-1}\color{blue}{+1-x } & = & 2 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 2 \color{blue}{+1} \\\Leftrightarrow &-8x & = &3\\\Leftrightarrow & \color{red}{-8}x & = &3\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{3}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{+8}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+8}\color{blue}{-8-x } & = & -3 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -3 \color{blue}{-8} \\\Leftrightarrow &-4x & = &-11\\\Leftrightarrow & \color{red}{-4}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-11}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{11}{4} } & & \\ & V = \left\{ \frac{11}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{+1}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+1}\color{blue}{-1-x } & = & 5 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 5 \color{blue}{-1} \\\Leftrightarrow &-16x & = &4\\\Leftrightarrow & \color{red}{-16}x & = &4\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{4}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{+8}& = & 9 \color{red}{ +11x } \\\Leftrightarrow & 13x \color{red}{+8}\color{blue}{-8-11x } & = & 9 \color{red}{ +11x }\color{blue}{-8-11x } \\\Leftrightarrow & 13x \color{blue}{-11x } & = & 9 \color{blue}{-8} \\\Leftrightarrow &2x & = &1\\\Leftrightarrow & \color{red}{2}x & = &1\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{1}{2} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{-12}& = & -5 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{-12}\color{blue}{+12-12x } & = & -5 \color{red}{ +12x }\color{blue}{+12-12x } \\\Leftrightarrow & -11x \color{blue}{-12x } & = & -5 \color{blue}{+12} \\\Leftrightarrow &-23x & = &7\\\Leftrightarrow & \color{red}{-23}x & = &7\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{7}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{23} } & & \\ & V = \left\{ \frac{-7}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{+10}& = & -11 \color{red}{ +13x } \\\Leftrightarrow & 15x \color{red}{+10}\color{blue}{-10-13x } & = & -11 \color{red}{ +13x }\color{blue}{-10-13x } \\\Leftrightarrow & 15x \color{blue}{-13x } & = & -11 \color{blue}{-10} \\\Leftrightarrow &2x & = &-21\\\Leftrightarrow & \color{red}{2}x & = &-21\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-21}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{2} } & & \\ & V = \left\{ \frac{-21}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{+10}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+10}\color{blue}{-10-x } & = & 1 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 1 \color{blue}{-10} \\\Leftrightarrow &-10x & = &-9\\\Leftrightarrow & \color{red}{-10}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-9}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{9}{10} } & & \\ & V = \left\{ \frac{9}{10} \right\} & \\\end{align}\)