Question 56 of 58intermediate🔧 ApplyNumerical2 marks

Find the rational number xx such that: 56(x+35)=56x+12\frac{5}{6}\left(x + \frac{3}{5}\right) = \frac{5}{6}x + \frac{1}{2}.

Correct Answer

Any rational number

Exercise: Exercise Set 3.3 | Q: 8 | (Chapter: 10)
For More Understanding

Explanation

The equation simplifies to an identity using the distributive property. Since the left-hand side equals the right-hand side for any value of x, there is no single solution; x can be any rational number.

Solution Steps

  1. Step 1: Apply the distributive property to the LHS: 56(x+35)=56x+(56×35)\frac{5}{6}(x + \frac{3}{5}) = \frac{5}{6}x + (\frac{5}{6} \times \frac{3}{5})

  2. Step 2: Simplify the multiplication: 56×35=1530=12\frac{5}{6} \times \frac{3}{5} = \frac{15}{30} = \frac{1}{2}

  3. Step 3: Substitute this back into the equation: 56x+12=56x+12\frac{5}{6}x + \frac{1}{2} = \frac{5}{6}x + \frac{1}{2}

  4. Step 4: Since LHS equals RHS for all values of x, the equation is an identity. Therefore, x can be any rational number.

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