Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{-5}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-5}\color{blue}{+5-13x } & = & 14 \color{red}{ +13x }\color{blue}{+5-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 14 \color{blue}{+5} \\\Leftrightarrow &-25x & = &19\\\Leftrightarrow & \color{red}{-25}x & = &19\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{19}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{25} } & & \\ & V = \left\{ \frac{-19}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{-2}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-2}\color{blue}{+2-x } & = & 9 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 9 \color{blue}{+2} \\\Leftrightarrow &-12x & = &11\\\Leftrightarrow & \color{red}{-12}x & = &11\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{11}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{12} } & & \\ & V = \left\{ \frac{-11}{12} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{+12}& = & -3 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+12}\color{blue}{-12-5x } & = & -3 \color{red}{ +5x }\color{blue}{-12-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -3 \color{blue}{-12} \\\Leftrightarrow &7x & = &-15\\\Leftrightarrow & \color{red}{7}x & = &-15\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-15}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{7} } & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{+6}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+6}\color{blue}{-6-x } & = & 3 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & 3 \color{blue}{-6} \\\Leftrightarrow &9x & = &-3\\\Leftrightarrow & \color{red}{9}x & = &-3\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-3}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{-10}& = & 1 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{-10}\color{blue}{+10+11x } & = & 1 \color{red}{ -11x }\color{blue}{+10+11x } \\\Leftrightarrow & 14x \color{blue}{+11x } & = & 1 \color{blue}{+10} \\\Leftrightarrow &25x & = &11\\\Leftrightarrow & \color{red}{25}x & = &11\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{11}{25} \\\Leftrightarrow & \color{green}{ x = \frac{11}{25} } & & \\ & V = \left\{ \frac{11}{25} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{-4}& = & -7 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-4}\color{blue}{+4+13x } & = & -7 \color{red}{ -13x }\color{blue}{+4+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -7 \color{blue}{+4} \\\Leftrightarrow &27x & = &-3\\\Leftrightarrow & \color{red}{27}x & = &-3\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-3}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{9} } & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{-12}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-12}\color{blue}{+12-x } & = & 2 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 2 \color{blue}{+12} \\\Leftrightarrow &-9x & = &14\\\Leftrightarrow & \color{red}{-9}x & = &14\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{14}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{9} } & & \\ & V = \left\{ \frac{-14}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{+14}& = & 8 \color{red}{ +3x } \\\Leftrightarrow & 4x \color{red}{+14}\color{blue}{-14-3x } & = & 8 \color{red}{ +3x }\color{blue}{-14-3x } \\\Leftrightarrow & 4x \color{blue}{-3x } & = & 8 \color{blue}{-14} \\\Leftrightarrow &x & = &-6\\\Leftrightarrow & \color{red}{}x & = &-6\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -6 \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{-1}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-1}\color{blue}{+1-x } & = & -11 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -11 \color{blue}{+1} \\\Leftrightarrow &-13x & = &-10\\\Leftrightarrow & \color{red}{-13}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{-2}& = & -15 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{-2}\color{blue}{+2+13x } & = & -15 \color{red}{ -13x }\color{blue}{+2+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & -15 \color{blue}{+2} \\\Leftrightarrow &20x & = &-13\\\Leftrightarrow & \color{red}{20}x & = &-13\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-13}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{20} } & & \\ & V = \left\{ \frac{-13}{20} \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{+2}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+2}\color{blue}{-2-x } & = & 14 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 14 \color{blue}{-2} \\\Leftrightarrow &-3x & = &12\\\Leftrightarrow & \color{red}{-3}x & = &12\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{12}{-3} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{-8}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-8}\color{blue}{+8-x } & = & 15 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 15 \color{blue}{+8} \\\Leftrightarrow &-16x & = &23\\\Leftrightarrow & \color{red}{-16}x & = &23\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{23}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{16} } & & \\ & V = \left\{ \frac{-23}{16} \right\} & \\\end{align}\)