Page 147 - ICSE Math 6

13 Linear Equations in One

Variable

Key Concepts

• To Write a Given Statement in Algebraic Form • Solution of an Equation
• To Write a Statement for a Given Algebraic Form • Solving Linear Equations in One Variable
• Transposition of Terms of an Equation • Word Problems

To Write a Given Statement in Algebraic Form

To write a given statement in algebraic form, replace the words by letters and symbols. For example,
consider the statement, ‘x when subtracted from 7 gives 3’. It can be written in algebraic form as
7 – x = 3.

Example 1: Write the algebraic forms of the given statements.
(a) Seven added to y gives 20.
(b) Twice of x when divided by 5 is equal to 3.
(c) Five times of y increased by 5 equals 30.
(d) A number decreased by 5 gives 15.

Solution: (a) 7 + y = 20
2x
(b) = 3
5
(c) 5y + 5 = 30
(d) Substitute a variable, say x, for a number to get,
x – 5 = 15

To Write a Statement for a Given Algebraic Form
To write a statement for a given algebraic form, replace the letters and symbols by words. For example,
x + 5 = 6 can be written in words as, ‘five added to x gives 6’.

Example 2: Write suitable statements for the given algebraic forms.
(a) 7 – x = 5 (b) 2y + 50 = 100
5z 15
(c) = 6 (d) = 5
3 x
Solution: (a) x when subtracted from 7 gives 5.
(b) Twice of y when increased by 50 results in 100.

(c) Five times of z when divided by 3 is equal to 6.
(d) Fifteen divided by x equals 5.

Linear Equations in One Variable
An equation is a mathematical statement which shows the equality of two expressions. An equation
always has an equality (=) sign and the expression on the left hand side equals the expression on the
2
right hand side. For example, 2x – 4 = x + 2 and 5 – 3y = –1 are equations. A linear equation is

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