Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{+11}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+11}\color{blue}{-11-x } & = & 13 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 13 \color{blue}{-11} \\\Leftrightarrow &x & = &2\\\Leftrightarrow & \color{red}{}x & = &2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 2 \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{-11}& = & 2 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-11}\color{blue}{+11-13x } & = & 2 \color{red}{ +13x }\color{blue}{+11-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 2 \color{blue}{+11} \\\Leftrightarrow &-25x & = &13\\\Leftrightarrow & \color{red}{-25}x & = &13\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{13}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{25} } & & \\ & V = \left\{ \frac{-13}{25} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{+7}& = & -13 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{+7}\color{blue}{-7+13x } & = & -13 \color{red}{ -13x }\color{blue}{-7+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & -13 \color{blue}{-7} \\\Leftrightarrow &22x & = &-20\\\Leftrightarrow & \color{red}{22}x & = &-20\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-20}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{11} } & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{-4}& = & -12 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-4}\color{blue}{+4-13x } & = & -12 \color{red}{ +13x }\color{blue}{+4-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -12 \color{blue}{+4} \\\Leftrightarrow &-25x & = &-8\\\Leftrightarrow & \color{red}{-25}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-8}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{8}{25} } & & \\ & V = \left\{ \frac{8}{25} \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{+7}& = & -5 \color{red}{ +15x } \\\Leftrightarrow & -x \color{red}{+7}\color{blue}{-7-15x } & = & -5 \color{red}{ +15x }\color{blue}{-7-15x } \\\Leftrightarrow & -x \color{blue}{-15x } & = & -5 \color{blue}{-7} \\\Leftrightarrow &-16x & = &-12\\\Leftrightarrow & \color{red}{-16}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-12}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{+5}& = & 1 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{+5}\color{blue}{-5-6x } & = & 1 \color{red}{ +6x }\color{blue}{-5-6x } \\\Leftrightarrow & -11x \color{blue}{-6x } & = & 1 \color{blue}{-5} \\\Leftrightarrow &-17x & = &-4\\\Leftrightarrow & \color{red}{-17}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-4}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{4}{17} } & & \\ & V = \left\{ \frac{4}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{+8}& = & 14 \color{red}{ -6x } \\\Leftrightarrow & x \color{red}{+8}\color{blue}{-8+6x } & = & 14 \color{red}{ -6x }\color{blue}{-8+6x } \\\Leftrightarrow & x \color{blue}{+6x } & = & 14 \color{blue}{-8} \\\Leftrightarrow &7x & = &6\\\Leftrightarrow & \color{red}{7}x & = &6\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{6}{7} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{+9}& = & 4 \color{red}{ +13x } \\\Leftrightarrow & 8x \color{red}{+9}\color{blue}{-9-13x } & = & 4 \color{red}{ +13x }\color{blue}{-9-13x } \\\Leftrightarrow & 8x \color{blue}{-13x } & = & 4 \color{blue}{-9} \\\Leftrightarrow &-5x & = &-5\\\Leftrightarrow & \color{red}{-5}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-5}{-5} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{-8}& = & 10 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{-8}\color{blue}{+8-8x } & = & 10 \color{red}{ +8x }\color{blue}{+8-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & 10 \color{blue}{+8} \\\Leftrightarrow &-23x & = &18\\\Leftrightarrow & \color{red}{-23}x & = &18\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{18}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{23} } & & \\ & V = \left\{ \frac{-18}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{-14}& = & -4 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{-14}\color{blue}{+14+8x } & = & -4 \color{red}{ -8x }\color{blue}{+14+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & -4 \color{blue}{+14} \\\Leftrightarrow &17x & = &10\\\Leftrightarrow & \color{red}{17}x & = &10\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{10}{17} \\\Leftrightarrow & \color{green}{ x = \frac{10}{17} } & & \\ & V = \left\{ \frac{10}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{-1}& = & 2 \color{red}{ +13x } \\\Leftrightarrow & -2x \color{red}{-1}\color{blue}{+1-13x } & = & 2 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & -2x \color{blue}{-13x } & = & 2 \color{blue}{+1} \\\Leftrightarrow &-15x & = &3\\\Leftrightarrow & \color{red}{-15}x & = &3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{+10}& = & 2 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{+10}\color{blue}{-10-13x } & = & 2 \color{red}{ +13x }\color{blue}{-10-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & 2 \color{blue}{-10} \\\Leftrightarrow &-17x & = &-8\\\Leftrightarrow & \color{red}{-17}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-8}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{8}{17} } & & \\ & V = \left\{ \frac{8}{17} \right\} & \\\end{align}\)