Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{-7}& = & 8 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{-7}\color{blue}{+7-13x } & = & 8 \color{red}{ +13x }\color{blue}{+7-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & 8 \color{blue}{+7} \\\Leftrightarrow &-16x & = &15\\\Leftrightarrow & \color{red}{-16}x & = &15\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{15}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{16} } & & \\ & V = \left\{ \frac{-15}{16} \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{-13}& = & 4 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{-13}\color{blue}{+13+13x } & = & 4 \color{red}{ -13x }\color{blue}{+13+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & 4 \color{blue}{+13} \\\Leftrightarrow &20x & = &17\\\Leftrightarrow & \color{red}{20}x & = &17\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{17}{20} \\\Leftrightarrow & \color{green}{ x = \frac{17}{20} } & & \\ & V = \left\{ \frac{17}{20} \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{+4}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+4}\color{blue}{-4-x } & = & -8 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -8 \color{blue}{-4} \\\Leftrightarrow &-8x & = &-12\\\Leftrightarrow & \color{red}{-8}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-12}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{+14}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+14}\color{blue}{-14-x } & = & -7 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -7 \color{blue}{-14} \\\Leftrightarrow &-13x & = &-21\\\Leftrightarrow & \color{red}{-13}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-21}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{21}{13} } & & \\ & V = \left\{ \frac{21}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{+1}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+1}\color{blue}{-1-13x } & = & 9 \color{red}{ +13x }\color{blue}{-1-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 9 \color{blue}{-1} \\\Leftrightarrow &-25x & = &8\\\Leftrightarrow & \color{red}{-25}x & = &8\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{8}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{25} } & & \\ & V = \left\{ \frac{-8}{25} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{-2}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-2}\color{blue}{+2-x } & = & -11 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -11 \color{blue}{+2} \\\Leftrightarrow &x & = &-9\\\Leftrightarrow & \color{red}{}x & = &-9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -9 \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{+4}& = & -7 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{+4}\color{blue}{-4+15x } & = & -7 \color{red}{ -15x }\color{blue}{-4+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & -7 \color{blue}{-4} \\\Leftrightarrow &23x & = &-11\\\Leftrightarrow & \color{red}{23}x & = &-11\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-11}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{23} } & & \\ & V = \left\{ \frac{-11}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{-9}& = & 10 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-9}\color{blue}{+9-9x } & = & 10 \color{red}{ +9x }\color{blue}{+9-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & 10 \color{blue}{+9} \\\Leftrightarrow &-13x & = &19\\\Leftrightarrow & \color{red}{-13}x & = &19\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{19}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{13} } & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{-1}& = & -11 \color{red}{ +3x } \\\Leftrightarrow & 7x \color{red}{-1}\color{blue}{+1-3x } & = & -11 \color{red}{ +3x }\color{blue}{+1-3x } \\\Leftrightarrow & 7x \color{blue}{-3x } & = & -11 \color{blue}{+1} \\\Leftrightarrow &4x & = &-10\\\Leftrightarrow & \color{red}{4}x & = &-10\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-10}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{+1}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+1}\color{blue}{-1-x } & = & -15 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -15 \color{blue}{-1} \\\Leftrightarrow &-5x & = &-16\\\Leftrightarrow & \color{red}{-5}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-16}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{16}{5} } & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{+7}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{+7}\color{blue}{-7-x } & = & -10 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & -10 \color{blue}{-7} \\\Leftrightarrow &2x & = &-17\\\Leftrightarrow & \color{red}{2}x & = &-17\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-17}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{2} } & & \\ & V = \left\{ \frac{-17}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{+9}& = & -3 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{+9}\color{blue}{-9-9x } & = & -3 \color{red}{ +9x }\color{blue}{-9-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & -3 \color{blue}{-9} \\\Leftrightarrow &5x & = &-12\\\Leftrightarrow & \color{red}{5}x & = &-12\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-12}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{5} } & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)