Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{-3}& = & 1 \color{red}{ +4x } \\\Leftrightarrow & 15x \color{red}{-3}\color{blue}{+3-4x } & = & 1 \color{red}{ +4x }\color{blue}{+3-4x } \\\Leftrightarrow & 15x \color{blue}{-4x } & = & 1 \color{blue}{+3} \\\Leftrightarrow &11x & = &4\\\Leftrightarrow & \color{red}{11}x & = &4\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{4}{11} \\\Leftrightarrow & \color{green}{ x = \frac{4}{11} } & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{-6}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-6}\color{blue}{+6-x } & = & 2 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 2 \color{blue}{+6} \\\Leftrightarrow &-5x & = &8\\\Leftrightarrow & \color{red}{-5}x & = &8\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{8}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{+11}& = & 12 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{+11}\color{blue}{-11+5x } & = & 12 \color{red}{ -5x }\color{blue}{-11+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & 12 \color{blue}{-11} \\\Leftrightarrow &16x & = &1\\\Leftrightarrow & \color{red}{16}x & = &1\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{1}{16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{16} } & & \\ & V = \left\{ \frac{1}{16} \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{-11}& = & 10 \color{red}{ +10x } \\\Leftrightarrow & -x \color{red}{-11}\color{blue}{+11-10x } & = & 10 \color{red}{ +10x }\color{blue}{+11-10x } \\\Leftrightarrow & -x \color{blue}{-10x } & = & 10 \color{blue}{+11} \\\Leftrightarrow &-11x & = &21\\\Leftrightarrow & \color{red}{-11}x & = &21\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{21}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{11} } & & \\ & V = \left\{ \frac{-21}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{+2}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+2}\color{blue}{-2-x } & = & -1 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -1 \color{blue}{-2} \\\Leftrightarrow &-4x & = &-3\\\Leftrightarrow & \color{red}{-4}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-3}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{-8}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-8}\color{blue}{+8-x } & = & 8 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 8 \color{blue}{+8} \\\Leftrightarrow &-9x & = &16\\\Leftrightarrow & \color{red}{-9}x & = &16\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{16}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{9} } & & \\ & V = \left\{ \frac{-16}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{+12}& = & 2 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+12}\color{blue}{-12+11x } & = & 2 \color{red}{ -11x }\color{blue}{-12+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 2 \color{blue}{-12} \\\Leftrightarrow &23x & = &-10\\\Leftrightarrow & \color{red}{23}x & = &-10\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-10}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{23} } & & \\ & V = \left\{ \frac{-10}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{+8}& = & 2 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+8}\color{blue}{-8-13x } & = & 2 \color{red}{ +13x }\color{blue}{-8-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 2 \color{blue}{-8} \\\Leftrightarrow &-25x & = &-6\\\Leftrightarrow & \color{red}{-25}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-6}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{6}{25} } & & \\ & V = \left\{ \frac{6}{25} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{+12}& = & 11 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{+12}\color{blue}{-12-9x } & = & 11 \color{red}{ +9x }\color{blue}{-12-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & 11 \color{blue}{-12} \\\Leftrightarrow &-20x & = &-1\\\Leftrightarrow & \color{red}{-20}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-1}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{1}{20} } & & \\ & V = \left\{ \frac{1}{20} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{-7}& = & -11 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{-7}\color{blue}{+7-5x } & = & -11 \color{red}{ +5x }\color{blue}{+7-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & -11 \color{blue}{+7} \\\Leftrightarrow &-17x & = &-4\\\Leftrightarrow & \color{red}{-17}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-4}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{4}{17} } & & \\ & V = \left\{ \frac{4}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{-10}& = & 15 \color{red}{ +13x } \\\Leftrightarrow & -2x \color{red}{-10}\color{blue}{+10-13x } & = & 15 \color{red}{ +13x }\color{blue}{+10-13x } \\\Leftrightarrow & -2x \color{blue}{-13x } & = & 15 \color{blue}{+10} \\\Leftrightarrow &-15x & = &25\\\Leftrightarrow & \color{red}{-15}x & = &25\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{25}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{+1}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+1}\color{blue}{-1-x } & = & 10 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 10 \color{blue}{-1} \\\Leftrightarrow &-12x & = &9\\\Leftrightarrow & \color{red}{-12}x & = &9\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{9}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)