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# State which of the following are equations (with a variable). Give a reason for your answer. Identify the variable from the equations with a variable.

(a) 17 = x + 7 (b) (t – 7) > 5 (c) 4 / 2 = 2 (d) (7 × 3) – 19 = 8 (e) 5 × 4 – 8 = 2x (f ) x – 2 = 0 (g) 2m < 30 (h) 2n + 1 = 11 (i) 7 = (11 × 5) – (12 × 4) ( j) 7 = (11 × 2) + p (k) 20 = 5y ( l) 3q / 2 < 5 (m) z + 12 > 24 (n) 20 – (10 – 5) = 3 × 5 (o) 7 – x = 5

**Solution:**

We use the concepts of algebra to answer the given questions.

A mathematical equation that represents the relationship between two expressions on either side of the equal sign (=) is a Simple Equation.

(a) 17 = x + 7 is an algebraic equation with variable x

(b) (t – 7) > 5 is an inequality and not an equation as it does not have = between the expressions on LHS and RHS

(c) 4 / 2 = 2 is a numerical equation which does not have a variable

(d) (7 × 3) – 19 = 8 is a numerical equation which does not have a variable

(e) 5 × 4 – 8 = 2x is an algebraic equation with variable x

(f) x – 2 = 0 is an algebraic equation with variable x

(g) 2m < 30 is an inequality and not an equation as it does not have = between the expressions on LHS and RHS

(h) 2n + 1 = 11 is an algebraic equation with variable n

(i) 7 = (11 × 5) – (12 × 4) is a numerical equation which does not have a variable

(j) 7 = (11 × 2) + p is an algebraic equation with variable p

(k) 20 = 5y is an algebraic equation with variable y

(l) 3q / 2 < 5 is an inequality and not an equation as it does not have = between the expressions on LHS and RHS

(m) z + 12 > 24 is an inequality and not an equation as it does not have = between the expressions on LHS and RHS

(n) 20 - (10 – 5) = 3 × 5 is a numerical equation which does not have any variable

(o) 7 – x = 5 is an algebraic equation with variable x

NCERT Solutions for Class 6 Maths Chapter 11 Exercise 11.5 Question 1

## State which of the following are equations (with a variable). Give reason for your answer. Identify the variable from the equations with a variable. (a) 17 = x + 7 (b) (t – 7) > 5 (c) 4 / 2 = 2 (d) (7 × 3) – 19 = 8 (e) 5 × 4 – 8 = 2x (f ) x – 2 = 0 (g) 2m < 30 (h) 2n + 1 = 11 (i) 7 = (11 × 5) – (12 × 4) ( j) 7 = (11 × 2) + p (k) 20 = 5y ( l) 3q / 2 < 5 (m) z + 12 > 24 (n) 20 – (10 – 5) = 3 × 5 (o) 7 – x = 5

**Summary:**

(a) 17 = x + 7 is an algebraic equation with variable x (b) (t – 7) > 5 is an inequality and not an equation as it does not have = between the expressions on LHS and RHS (c) 4 / 2 = 2 is a numerical equation which does not have a variable (d) (7 × 3) – 19 = 8 is a numerical equation which does not have a variable (e) 5 × 4 – 8 = 2x is an algebraic equation with variable x (f) x – 2 = 0 is an algebraic equation with variable x (g) 2m < 30 is an inequality and not an equation as it does not have = between the expressions on LHS and RHS (h) 2n + 1 = 11 is an algebraic equation with variable n (i) 7 = (11 × 5) – (12 × 4) is a numerical equation which does not have a variable (j) 7 = (11 × 2) + p is an algebraic equation with variable p (k) 20 = 5y is an algebraic equation with variable y (l) 3q / 2 < 5 is an inequality and not an equation as it does not have = between the expressions on LHS and RHS (m) z + 12 > 24 is an inequality and not an equation as it does not have = between the expressions on LHS and RHS (n) 20 - (10 – 5) = 3 × 5 is a numerical equation which does not have any variable (o) 7 – x = 5 is an algebraic equation with variable x

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