Question 51 of 58beginner🔧 ApplyNumerical2 marks

If x3+x5=1615\frac{x}{3} + \frac{x}{5} = \frac{16}{15}, find the rational number xx.

Correct Answer

2

Exercise: END-OF-CHAPTER EXERCISES | Q: 8 | (Page 25)
For More Understanding

Explanation

To find the value of the rational number x, we solve the given linear equation by taking the LCM of the denominators on the left-hand side, simplifying the equation, and then isolating the variable x.

Solution Steps

  1. Step 1: Find the LCM and rewrite the equation - The LCM of the denominators 3 and 5 is 15. We rewrite the equation with this common denominator: 5x/15 + 3x/15 = 16/15

  2. Step 2: Add the fractions - We add the numerators on the left-hand side: (5x + 3x)/15 = 16/15

  3. Step 3: Simplify the equation - This simplifies to 8x/15 = 16/15. Since the denominators are equal, we equate the numerators: 8x = 16

  4. Step 4: Solve for x - Dividing both sides by 8, we get x = 2

PreviousNext