PREVIOUSLY ASKED IN:
CTET 2026
Answer
31
Explanation
First, simplify the inner bracket: \( 2x - \frac{1-x}{2} = \frac{4x - 1 + x}{2} = \frac{5x-1}{2} \). The equation becomes: \( \frac{7x-1}{4} - \frac{5x-1}{6} = \frac{10}{3} \). Multiply by LCM 12 to remove fractions: \( 3(7x-1) - 2(5x-1) = 40 \) \( \Rightarrow 21x - 3 - 10x + 2 = 40 \) \( \Rightarrow 11x - 1 = 40 \) \( \Rightarrow 11x = 41 \) \( \Rightarrow x = \frac{41}{11} \). Now find \( \frac{11x+21}{2} = \frac{11(\frac{41}{11}) + 21}{2} = \frac{41 + 21}{2} = 31 \).
Key Points
- > In linear equations, solve the nested fractions inside brackets first.
- > The easiest way to eliminate fractions is multiplying the entire equation by the LCM of all denominators.
- > Be extremely careful with signs when opening brackets preceded by a minus sign.
- > If \( x \) comes out as a fraction, don't panic; it often cancels out in the final expression.
- > Strictly follow the BODMAS rule while solving algebraic expressions.
- > Stay attentive while substituting the solved value into the final required expression.
- > This is a classic example of a Linear Equation in One Variable.
Additional Information
Equation Solving Strategies
| Equation Type | Highest Power | Number of Roots |
|---|---|---|
| Linear | 1 | 1 |
| Quadratic | 2 | 2 |
| Cubic | 3 | 3 |
| Simultaneous | 1 (Multiple vars) | 1 set (usually) |
Memory Tips
- LCM Trick: For denominators like 4, 6, and 3, multiplying the entire equation by their LCM (12) instantly removes all fractions.
- Sign Rule: Whenever a term crosses the '=' sign, its polarity changes (+ becomes -, and vice versa).