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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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