Algebraic Expressions And Inequalities Questions for SSC GD

Algebraic Expressions: Basics

An algebraic expression is a combination of variables, constants, and operations (addition, subtraction, multiplication, division). In SSC GD, you'll simplify expressions by combining like terms and applying order of operations. Like terms have the same variable raised to the same power — for example, 3x and 5x are like terms, but 3x and 3x^2 are not. Always remember BODMAS: Brackets, Orders (powers), Division, Multiplication, Addition, Subtraction.

• Like terms: same variable and same exponent — combine by adding/subtracting coefficients
• Unlike terms: cannot be combined — leave as separate terms
• Coefficient: the number multiplying the variable (in 5x, coefficient is 5)
• Constant: a term with no variable (the number 7 in 3x + 7)
• Simplify by grouping like terms and applying BODMAS order

Solving Linear Equations and Expressions

SSC GD often asks you to solve for a variable or simplify an expression by substitution. The key is isolating the variable on one side of the equals sign by performing the same operation on both sides. For example, if 2x + 3 = 11, subtract 3 from both sides to get 2x = 8, then divide by 2 to get x = 4. In substitution problems, replace the variable with the given value and calculate step by step.

• Isolate variable: move constants to one side, variables to the other
• Perform same operation on both sides to maintain equality
• Substitution: replace variable with given number and evaluate using BODMAS
• Check your answer by substituting back into the original equation
• Watch for negative signs — they flip when moving terms across the equals sign

Inequalities: Symbols and Rules

Inequalities compare two expressions using symbols: greater than (>), less than (<), greater than or equal to (>=), less than or equal to (<=). The critical rule in SSC GD questions is: when you multiply or divide both sides of an inequality by a negative number, flip the inequality symbol. For example, if -2x > 8, divide by -2 and flip: x < -4. Addition and subtraction do NOT flip the symbol.

• Symbols: > (greater), < (less), >= (greater or equal), <= (less or equal)
• Add/subtract same number on both sides — symbol stays the same
• Multiply/divide by positive number — symbol stays the same
• Multiply/divide by negative number — FLIP the symbol
• Transitive property: if a > b and b > c, then a > c

Factorization and Expansion

Factorization breaks an expression into its factors (numbers or expressions that multiply to give the original). Expansion does the opposite — multiplying factors to get a polynomial. SSC GD tests common patterns: difference of squares (a^2 - b^2 = (a+b)(a-b)), perfect squares (a^2 + 2ab + b^2 = (a+b)^2), and trinomials. These appear in simplification and inequality problems.

• Difference of squares: a^2 - b^2 = (a + b)(a - b)
• Perfect square trinomial: a^2 + 2ab + b^2 = (a + b)^2
• Perfect square trinomial: a^2 - 2ab + b^2 = (a - b)^2
• Trinomial: ax^2 + bx + c — find factors of ac that add to b
• Common factor: always pull out GCD of all terms first

Compound Inequalities and Number Line

Compound inequalities combine two inequalities with AND or OR. AND means both conditions must be true (the solution is the overlap). OR means at least one condition is true (the solution is the union). SSC GD may ask you to identify which values satisfy a compound inequality or to solve a system. Visualizing on a number line helps avoid mistakes.

• AND compound: both conditions true — solution is the intersection (overlap)
• OR compound: at least one true — solution is the union (combined range)
• Closed dot on number line: value is included (>= or <=)
• Open dot on number line: value is excluded (> or <)
• Write solution in interval notation or inequality form

• Forgetting to flip the inequality symbol when multiplying/dividing by a negative — this is the #1 error in SSC GD inequality questions.
• Combining unlike terms (e.g., treating 3x + 3x^2 as 6x^2) — always check that exponents match before combining.
• Misapplying BODMAS in substitution — calculate powers before multiplication, not after.
• Misreading compound inequalities — confusing AND (overlap) with OR (union) leads to wrong solution ranges.
• Careless sign errors when moving terms across the equals sign — subtract becomes add, multiply becomes divide.

• FLIP on NEGATIVE: When you multiply or divide an inequality by a negative number, FLIP the symbol. Think: the number line flips direction.
• BODMAS = Brackets, Orders, Division/Multiplication (left to right), Addition/Subtraction (left to right). Always follow this order.
• Like Terms = Same Variable + Same Exponent. If exponents differ, they are UNLIKE and cannot be combined.
• Difference of Squares = (a+b)(a-b). Perfect Squares = (a+b)^2 or (a-b)^2. These are the two most tested factorization patterns in SSC GD.

• SSC GD typically includes 1-2 direct simplification questions (substitute and calculate) and 1-2 inequality or equation-solving questions per paper.
• Recent papers show preference for negative numbers in inequalities — this tests whether you remember to flip the symbol. Practice these heavily.
• Factorization questions often appear as part of larger simplification — recognize difference of squares and perfect squares instantly to save time.
• Compound inequalities are less common but high-accuracy scoring. If you see one, take 30 seconds to draw a number line — it prevents careless errors.
• Time management: algebraic expression questions are typically 1-2 minutes each. If stuck, move on and return — they are not worth excessive time.