Question

Find the number of solutions for the following equation:
$\frac{\text{9x}}{6}-\frac{\text{2x - 3}}{6}+1=5\text{x}+\frac{\text{2x + 4}}{6}$

• A. Zero solution
• B. Unique solution
• C. Infinite number of solutions
• D. Can't be determined

Answer 1

The correct option is B Unique solution

Given expression:
$\frac{\text{9x}}{6}-\frac{\text{2x - 3}}{6}+1=5\text{x}+\frac{\text{2x + 4}}{6}$

By taking the LCM,
$\frac{\text{9x}}{6}-\frac{\text{2x - 3}}{6}+\frac{6}{6}=\frac{30\text{x}}{6}+\frac{\text{2x + 4}}{6}$

The denominator of all the terms is 6. So, LCM is 6.

By removing the denominator

$\text{9x}-\text{2x + 3}+6=30\text{x}+\text{2x + 4}$

$⟹$ $\text{7x}+3+6=32\text{x}+4$

$⟹$ $\text{7x}+9=32\text{x}+4$

$⟹$ $\text{9 - 4 = 32x - 7x}$

$⟹$ $\text{5 = 25x}$

$⟹$ $\text{x}=\frac{5}{25}$

$⟹$ $\text{x}=\frac{1}{5}$

$\therefore$ The equation has a unique solution.