Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

---

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{-10}& = & -9 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-10}\color{blue}{+10+13x } & = & -9 \color{red}{ -13x }\color{blue}{+10+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -9 \color{blue}{+10} \\\Leftrightarrow &27x & = &1\\\Leftrightarrow & \color{red}{27}x & = &1\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{1}{27} \\\Leftrightarrow & \color{green}{ x = \frac{1}{27} } & & \\ & V = \left\{ \frac{1}{27} \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{+9}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+9}\color{blue}{-9-x } & = & -7 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -7 \color{blue}{-9} \\\Leftrightarrow &-15x & = &-16\\\Leftrightarrow & \color{red}{-15}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-16}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{16}{15} } & & \\ & V = \left\{ \frac{16}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{-13}& = & 5 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-13}\color{blue}{+13+11x } & = & 5 \color{red}{ -11x }\color{blue}{+13+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 5 \color{blue}{+13} \\\Leftrightarrow &23x & = &18\\\Leftrightarrow & \color{red}{23}x & = &18\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{18}{23} \\\Leftrightarrow & \color{green}{ x = \frac{18}{23} } & & \\ & V = \left\{ \frac{18}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{-9}& = & 6 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{-9}\color{blue}{+9+7x } & = & 6 \color{red}{ -7x }\color{blue}{+9+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & 6 \color{blue}{+9} \\\Leftrightarrow &11x & = &15\\\Leftrightarrow & \color{red}{11}x & = &15\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{15}{11} \\\Leftrightarrow & \color{green}{ x = \frac{15}{11} } & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{+11}& = & 14 \color{red}{ +4x } \\\Leftrightarrow & 5x \color{red}{+11}\color{blue}{-11-4x } & = & 14 \color{red}{ +4x }\color{blue}{-11-4x } \\\Leftrightarrow & 5x \color{blue}{-4x } & = & 14 \color{blue}{-11} \\\Leftrightarrow &x & = &3\\\Leftrightarrow & \color{red}{}x & = &3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 3 \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{-13}& = & -9 \color{red}{ -7x } \\\Leftrightarrow & 5x \color{red}{-13}\color{blue}{+13+7x } & = & -9 \color{red}{ -7x }\color{blue}{+13+7x } \\\Leftrightarrow & 5x \color{blue}{+7x } & = & -9 \color{blue}{+13} \\\Leftrightarrow &12x & = &4\\\Leftrightarrow & \color{red}{12}x & = &4\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{4}{12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{+9}& = & 1 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{+9}\color{blue}{-9-8x } & = & 1 \color{red}{ +8x }\color{blue}{-9-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & 1 \color{blue}{-9} \\\Leftrightarrow &-23x & = &-8\\\Leftrightarrow & \color{red}{-23}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-8}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{8}{23} } & & \\ & V = \left\{ \frac{8}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{+9}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+9}\color{blue}{-9-x } & = & 2 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 2 \color{blue}{-9} \\\Leftrightarrow &-5x & = &-7\\\Leftrightarrow & \color{red}{-5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{+5}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+5}\color{blue}{-5-x } & = & -1 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -1 \color{blue}{-5} \\\Leftrightarrow &-4x & = &-6\\\Leftrightarrow & \color{red}{-4}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-6}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{-11}& = & -5 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-11}\color{blue}{+11-13x } & = & -5 \color{red}{ +13x }\color{blue}{+11-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -5 \color{blue}{+11} \\\Leftrightarrow &-28x & = &6\\\Leftrightarrow & \color{red}{-28}x & = &6\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{6}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{14} } & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{-3}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-3}\color{blue}{+3-x } & = & 13 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 13 \color{blue}{+3} \\\Leftrightarrow &-9x & = &16\\\Leftrightarrow & \color{red}{-9}x & = &16\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{16}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{9} } & & \\ & V = \left\{ \frac{-16}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{-1}& = & 9 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-1}\color{blue}{+1-7x } & = & 9 \color{red}{ +7x }\color{blue}{+1-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 9 \color{blue}{+1} \\\Leftrightarrow &-17x & = &10\\\Leftrightarrow & \color{red}{-17}x & = &10\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{10}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{17} } & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)