Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{-1}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-1}\color{blue}{+1-x } & = & 9 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 9 \color{blue}{+1} \\\Leftrightarrow &7x & = &10\\\Leftrightarrow & \color{red}{7}x & = &10\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{10}{7} \\\Leftrightarrow & \color{green}{ x = \frac{10}{7} } & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{+14}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+14}\color{blue}{-14-x } & = & -13 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -13 \color{blue}{-14} \\\Leftrightarrow &-7x & = &-27\\\Leftrightarrow & \color{red}{-7}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-27}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{27}{7} } & & \\ & V = \left\{ \frac{27}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{+15}& = & -12 \color{red}{ -2x } \\\Leftrightarrow & 13x \color{red}{+15}\color{blue}{-15+2x } & = & -12 \color{red}{ -2x }\color{blue}{-15+2x } \\\Leftrightarrow & 13x \color{blue}{+2x } & = & -12 \color{blue}{-15} \\\Leftrightarrow &15x & = &-27\\\Leftrightarrow & \color{red}{15}x & = &-27\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-27}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{-3}& = & 13 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{-3}\color{blue}{+3+13x } & = & 13 \color{red}{ -13x }\color{blue}{+3+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & 13 \color{blue}{+3} \\\Leftrightarrow &24x & = &16\\\Leftrightarrow & \color{red}{24}x & = &16\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{16}{24} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{-7}& = & 8 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{-7}\color{blue}{+7-13x } & = & 8 \color{red}{ +13x }\color{blue}{+7-13x } \\\Leftrightarrow & 12x \color{blue}{-13x } & = & 8 \color{blue}{+7} \\\Leftrightarrow &-x & = &15\\\Leftrightarrow & \color{red}{-}x & = &15\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{15}{-1} \\\Leftrightarrow & \color{green}{ x = -15 } & & \\ & V = \left\{ -15 \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{-9}& = & -8 \color{red}{ +13x } \\\Leftrightarrow & -2x \color{red}{-9}\color{blue}{+9-13x } & = & -8 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & -2x \color{blue}{-13x } & = & -8 \color{blue}{+9} \\\Leftrightarrow &-15x & = &1\\\Leftrightarrow & \color{red}{-15}x & = &1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{15} } & & \\ & V = \left\{ \frac{-1}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{+7}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+7}\color{blue}{-7-x } & = & 15 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 15 \color{blue}{-7} \\\Leftrightarrow &-8x & = &8\\\Leftrightarrow & \color{red}{-8}x & = &8\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{8}{-8} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{+4}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+4}\color{blue}{-4-x } & = & -4 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -4 \color{blue}{-4} \\\Leftrightarrow &-6x & = &-8\\\Leftrightarrow & \color{red}{-6}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-8}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{+3}& = & 9 \color{red}{ +8x } \\\Leftrightarrow & 5x \color{red}{+3}\color{blue}{-3-8x } & = & 9 \color{red}{ +8x }\color{blue}{-3-8x } \\\Leftrightarrow & 5x \color{blue}{-8x } & = & 9 \color{blue}{-3} \\\Leftrightarrow &-3x & = &6\\\Leftrightarrow & \color{red}{-3}x & = &6\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{6}{-3} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{-15}& = & -5 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-15}\color{blue}{+15-7x } & = & -5 \color{red}{ +7x }\color{blue}{+15-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -5 \color{blue}{+15} \\\Leftrightarrow &-17x & = &10\\\Leftrightarrow & \color{red}{-17}x & = &10\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{10}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{17} } & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{+8}& = & 2 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+8}\color{blue}{-8-x } & = & 2 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & 2 \color{blue}{-8} \\\Leftrightarrow &9x & = &-6\\\Leftrightarrow & \color{red}{9}x & = &-6\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-6}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{+6}& = & -10 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{+6}\color{blue}{-6-3x } & = & -10 \color{red}{ +3x }\color{blue}{-6-3x } \\\Leftrightarrow & -2x \color{blue}{-3x } & = & -10 \color{blue}{-6} \\\Leftrightarrow &-5x & = &-16\\\Leftrightarrow & \color{red}{-5}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-16}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{16}{5} } & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)