Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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