Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{+9}& = & 2 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{+9}\color{blue}{-9-7x } & = & 2 \color{red}{ +7x }\color{blue}{-9-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & 2 \color{blue}{-9} \\\Leftrightarrow &-5x & = &-7\\\Leftrightarrow & \color{red}{-5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{+8}& = & 2 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{+8}\color{blue}{-8+4x } & = & 2 \color{red}{ -4x }\color{blue}{-8+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & 2 \color{blue}{-8} \\\Leftrightarrow &13x & = &-6\\\Leftrightarrow & \color{red}{13}x & = &-6\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-6}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{-5}& = & 12 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-5}\color{blue}{+5-9x } & = & 12 \color{red}{ +9x }\color{blue}{+5-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 12 \color{blue}{+5} \\\Leftrightarrow &-17x & = &17\\\Leftrightarrow & \color{red}{-17}x & = &17\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{17}{-17} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{+15}& = & 5 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+15}\color{blue}{-15+11x } & = & 5 \color{red}{ -11x }\color{blue}{-15+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 5 \color{blue}{-15} \\\Leftrightarrow &17x & = &-10\\\Leftrightarrow & \color{red}{17}x & = &-10\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-10}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{17} } & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{+7}& = & -11 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+7}\color{blue}{-7-13x } & = & -11 \color{red}{ +13x }\color{blue}{-7-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -11 \color{blue}{-7} \\\Leftrightarrow &-28x & = &-18\\\Leftrightarrow & \color{red}{-28}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-18}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{9}{14} } & & \\ & V = \left\{ \frac{9}{14} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{-14}& = & 7 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{-14}\color{blue}{+14+14x } & = & 7 \color{red}{ -14x }\color{blue}{+14+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & 7 \color{blue}{+14} \\\Leftrightarrow &19x & = &21\\\Leftrightarrow & \color{red}{19}x & = &21\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{21}{19} \\\Leftrightarrow & \color{green}{ x = \frac{21}{19} } & & \\ & V = \left\{ \frac{21}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{-7}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & x \color{red}{-7}\color{blue}{+7-13x } & = & 9 \color{red}{ +13x }\color{blue}{+7-13x } \\\Leftrightarrow & x \color{blue}{-13x } & = & 9 \color{blue}{+7} \\\Leftrightarrow &-12x & = &16\\\Leftrightarrow & \color{red}{-12}x & = &16\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{16}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{+5}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+5}\color{blue}{-5-x } & = & -13 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -13 \color{blue}{-5} \\\Leftrightarrow &-10x & = &-18\\\Leftrightarrow & \color{red}{-10}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-18}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{+15}& = & 14 \color{red}{ +4x } \\\Leftrightarrow & 11x \color{red}{+15}\color{blue}{-15-4x } & = & 14 \color{red}{ +4x }\color{blue}{-15-4x } \\\Leftrightarrow & 11x \color{blue}{-4x } & = & 14 \color{blue}{-15} \\\Leftrightarrow &7x & = &-1\\\Leftrightarrow & \color{red}{7}x & = &-1\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-1}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{-4}& = & -15 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{-4}\color{blue}{+4-12x } & = & -15 \color{red}{ +12x }\color{blue}{+4-12x } \\\Leftrightarrow & -11x \color{blue}{-12x } & = & -15 \color{blue}{+4} \\\Leftrightarrow &-23x & = &-11\\\Leftrightarrow & \color{red}{-23}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-11}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{11}{23} } & & \\ & V = \left\{ \frac{11}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{+7}& = & -12 \color{red}{ +2x } \\\Leftrightarrow & x \color{red}{+7}\color{blue}{-7-2x } & = & -12 \color{red}{ +2x }\color{blue}{-7-2x } \\\Leftrightarrow & x \color{blue}{-2x } & = & -12 \color{blue}{-7} \\\Leftrightarrow &-x & = &-19\\\Leftrightarrow & \color{red}{-}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-19}{-1} \\\Leftrightarrow & \color{green}{ x = 19 } & & \\ & V = \left\{ 19 \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{+15}& = & -13 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+15}\color{blue}{-15-7x } & = & -13 \color{red}{ +7x }\color{blue}{-15-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & -13 \color{blue}{-15} \\\Leftrightarrow &3x & = &-28\\\Leftrightarrow & \color{red}{3}x & = &-28\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-28}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-28}{3} } & & \\ & V = \left\{ \frac{-28}{3} \right\} & \\\end{align}\)