Question

Identify the equalities and the equations in the following statements.

(1) x − 2 = 7
(2) 4x = 20
(3) $2=\frac{10}{5}$
(4) $2=\frac{10}{x}$
(5) 18 = 10 + x
(6) 9(8 − 3) = 9 × 8 − 9 × 3

Answer 1

(1) In the given statement, if put x = 9, we will get:
LHS = RHS (∵ 9 – 2 = 7)
Because an equation is a condition to find the value of a variable, the statement is the equation.

(2) In the given statement, if we put x = 5, we will get:
LHS = RHS (∵ 4 × 5 = 20)
Because an equation is a condition to find the value of a variable, the statement is the equation.

(3) $\frac{10}{5}=2$
In the given statement, the expression on the left-hand side and that on the right-hand side of the ‘=’ sign are equal, so the statement is an equality.

(4) In the given statement, if we put x = 5, we will get:
LHS = RHS. $\left(\because \frac{10}{5}=2\right)$
Because an equation is a condition to find the value of a variable, the statement is an equation.

(5) In the given statement, if we put x = 8, we will get:
LHS = RHS (∵ 10 + 8 = 18)
Because an equation is a condition to find the value of a variable, the statement is an equation.

(6) The expression on the LHS can be solved as:
9 (8 – 3) (Performing subtraction in the simple brackets first)
= 9 × 5
= 45
The expression on the RHS can be solved as:
9 × 8 – 9 × 3
= 72 – 27 (Performing multiplication first)
= 4
The expression on the left-hand side and that on the right-hand side of the ‘=’ sign are equal, so the statement is an equality.