Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{-3}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{-3}\color{blue}{+3-13x } & = & 11 \color{red}{ +13x }\color{blue}{+3-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & 11 \color{blue}{+3} \\\Leftrightarrow &-17x & = &14\\\Leftrightarrow & \color{red}{-17}x & = &14\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{14}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{17} } & & \\ & V = \left\{ \frac{-14}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{+13}& = & 6 \color{red}{ +13x } \\\Leftrightarrow & x \color{red}{+13}\color{blue}{-13-13x } & = & 6 \color{red}{ +13x }\color{blue}{-13-13x } \\\Leftrightarrow & x \color{blue}{-13x } & = & 6 \color{blue}{-13} \\\Leftrightarrow &-12x & = &-7\\\Leftrightarrow & \color{red}{-12}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-7}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{12} } & & \\ & V = \left\{ \frac{7}{12} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{+10}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & 11x \color{red}{+10}\color{blue}{-10-7x } & = & -3 \color{red}{ +7x }\color{blue}{-10-7x } \\\Leftrightarrow & 11x \color{blue}{-7x } & = & -3 \color{blue}{-10} \\\Leftrightarrow &4x & = &-13\\\Leftrightarrow & \color{red}{4}x & = &-13\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-13}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{4} } & & \\ & V = \left\{ \frac{-13}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{+7}& = & -7 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+7}\color{blue}{-7+6x } & = & -7 \color{red}{ -6x }\color{blue}{-7+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -7 \color{blue}{-7} \\\Leftrightarrow &19x & = &-14\\\Leftrightarrow & \color{red}{19}x & = &-14\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-14}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{19} } & & \\ & V = \left\{ \frac{-14}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{+2}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{+2}\color{blue}{-2-x } & = & 7 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 5x \color{blue}{-x } & = & 7 \color{blue}{-2} \\\Leftrightarrow &4x & = &5\\\Leftrightarrow & \color{red}{4}x & = &5\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{5}{4} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{-11}& = & 3 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{-11}\color{blue}{+11-11x } & = & 3 \color{red}{ +11x }\color{blue}{+11-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & 3 \color{blue}{+11} \\\Leftrightarrow &-5x & = &14\\\Leftrightarrow & \color{red}{-5}x & = &14\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{14}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{5} } & & \\ & V = \left\{ \frac{-14}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{-7}& = & -4 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{-7}\color{blue}{+7+11x } & = & -4 \color{red}{ -11x }\color{blue}{+7+11x } \\\Leftrightarrow & 14x \color{blue}{+11x } & = & -4 \color{blue}{+7} \\\Leftrightarrow &25x & = &3\\\Leftrightarrow & \color{red}{25}x & = &3\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{3}{25} \\\Leftrightarrow & \color{green}{ x = \frac{3}{25} } & & \\ & V = \left\{ \frac{3}{25} \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{+9}& = & -5 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+9}\color{blue}{-9-x } & = & -5 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -5 \color{blue}{-9} \\\Leftrightarrow &5x & = &-14\\\Leftrightarrow & \color{red}{5}x & = &-14\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-14}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{5} } & & \\ & V = \left\{ \frac{-14}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{-9}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-9}\color{blue}{+9-x } & = & 9 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 9 \color{blue}{+9} \\\Leftrightarrow &-5x & = &18\\\Leftrightarrow & \color{red}{-5}x & = &18\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{18}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{5} } & & \\ & V = \left\{ \frac{-18}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{+3}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+3}\color{blue}{-3-x } & = & -4 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -4 \color{blue}{-3} \\\Leftrightarrow &x & = &-7\\\Leftrightarrow & \color{red}{}x & = &-7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -7 \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{+13}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+13}\color{blue}{-13-x } & = & -6 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -6 \color{blue}{-13} \\\Leftrightarrow &-15x & = &-19\\\Leftrightarrow & \color{red}{-15}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-19}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{19}{15} } & & \\ & V = \left\{ \frac{19}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{-13}& = & -8 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{-13}\color{blue}{+13+12x } & = & -8 \color{red}{ -12x }\color{blue}{+13+12x } \\\Leftrightarrow & 5x \color{blue}{+12x } & = & -8 \color{blue}{+13} \\\Leftrightarrow &17x & = &5\\\Leftrightarrow & \color{red}{17}x & = &5\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{5}{17} \\\Leftrightarrow & \color{green}{ x = \frac{5}{17} } & & \\ & V = \left\{ \frac{5}{17} \right\} & \\\end{align}\)