Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{-14}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{-14}\color{blue}{+14-x } & = & 15 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & 15 \color{blue}{+14} \\\Leftrightarrow &2x & = &29\\\Leftrightarrow & \color{red}{2}x & = &29\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{29}{2} \\\Leftrightarrow & \color{green}{ x = \frac{29}{2} } & & \\ & V = \left\{ \frac{29}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{-11}& = & 10 \color{red}{ -x } \\\Leftrightarrow & x \color{red}{-11}\color{blue}{+11+x } & = & 10 \color{red}{ -x }\color{blue}{+11+x } \\\Leftrightarrow & x \color{blue}{+x } & = & 10 \color{blue}{+11} \\\Leftrightarrow &2x & = &21\\\Leftrightarrow & \color{red}{2}x & = &21\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{21}{2} \\\Leftrightarrow & \color{green}{ x = \frac{21}{2} } & & \\ & V = \left\{ \frac{21}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{+8}& = & 1 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+8}\color{blue}{-8+13x } & = & 1 \color{red}{ -13x }\color{blue}{-8+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & 1 \color{blue}{-8} \\\Leftrightarrow &20x & = &-7\\\Leftrightarrow & \color{red}{20}x & = &-7\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-7}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{20} } & & \\ & V = \left\{ \frac{-7}{20} \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{+12}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+12}\color{blue}{-12-x } & = & 5 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 5 \color{blue}{-12} \\\Leftrightarrow &-3x & = &-7\\\Leftrightarrow & \color{red}{-3}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-7}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{+14}& = & 5 \color{red}{ +5x } \\\Leftrightarrow & 9x \color{red}{+14}\color{blue}{-14-5x } & = & 5 \color{red}{ +5x }\color{blue}{-14-5x } \\\Leftrightarrow & 9x \color{blue}{-5x } & = & 5 \color{blue}{-14} \\\Leftrightarrow &4x & = &-9\\\Leftrightarrow & \color{red}{4}x & = &-9\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-9}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{4} } & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{-5}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-5}\color{blue}{+5-x } & = & 8 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 8 \color{blue}{+5} \\\Leftrightarrow &-10x & = &13\\\Leftrightarrow & \color{red}{-10}x & = &13\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{13}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{10} } & & \\ & V = \left\{ \frac{-13}{10} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{-13}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-13}\color{blue}{+13-x } & = & 8 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 8 \color{blue}{+13} \\\Leftrightarrow &-3x & = &21\\\Leftrightarrow & \color{red}{-3}x & = &21\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{21}{-3} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{-14}& = & 1 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-14}\color{blue}{+14-7x } & = & 1 \color{red}{ +7x }\color{blue}{+14-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 1 \color{blue}{+14} \\\Leftrightarrow &3x & = &15\\\Leftrightarrow & \color{red}{3}x & = &15\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{15}{3} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{+4}& = & -1 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+4}\color{blue}{-4-13x } & = & -1 \color{red}{ +13x }\color{blue}{-4-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -1 \color{blue}{-4} \\\Leftrightarrow &-25x & = &-5\\\Leftrightarrow & \color{red}{-25}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-5}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{+13}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+13}\color{blue}{-13-x } & = & -6 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -6 \color{blue}{-13} \\\Leftrightarrow &-6x & = &-19\\\Leftrightarrow & \color{red}{-6}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-19}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{19}{6} } & & \\ & V = \left\{ \frac{19}{6} \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{+6}& = & -11 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+6}\color{blue}{-6-13x } & = & -11 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -11 \color{blue}{-6} \\\Leftrightarrow &-25x & = &-17\\\Leftrightarrow & \color{red}{-25}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-17}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{17}{25} } & & \\ & V = \left\{ \frac{17}{25} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{+9}& = & -9 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+9}\color{blue}{-9+11x } & = & -9 \color{red}{ -11x }\color{blue}{-9+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -9 \color{blue}{-9} \\\Leftrightarrow &17x & = &-18\\\Leftrightarrow & \color{red}{17}x & = &-18\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-18}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{17} } & & \\ & V = \left\{ \frac{-18}{17} \right\} & \\\end{align}\)