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1. Express the mathematical statement ‘3 added to one-third of x gives 30’ in a simple equation.

2. Write the simple equation 4y – 2 = 18 in statement form.
3. Kanav found the solution of 11 + 2p = 19 as 5. Do you agree with the answer? Verify.

x
4. Find the value of x, if 5 × 3000 + x = 5 × 6000 + .
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Linear Equations

A mathematical statement equating two algebraic expressions is called an algebraic equation.
The expression on the LHS is separated from the expression on the RHS by an equal (=) sign.

Expressions may have one or more variables.
Remember
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For example, x + 4 = 5, y + 3 = 7, x + 2y = 8, xy + 6z = 4, etc.
In linear equations, the highest
An equation is called a linear equation, when the highest power power of the variable in each term
of the variable involved is 1. For example, 2x – 7 = 5, 3x + y = 7, is 1.
1
3 x + 1 = y, etc.
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Linear Equations in One Variable

An algebraic equation with only one variable having highest
power 1 is called a linear equation in one variable. For Quick Check
example, x + 4 = 7, 2x – 7 = 9, 5z + 9 = 4z, etc. Which of the following is
Thus, a linear equation in one variable can be expressed in a linear equation with one
the form of ax + b = 0, where ‘a’ and ‘b’ are rational numbers variable?
and ‘x’ is the variable. 1. 3x – 7y = 8 2. 5x – 6 = 9
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Solution of a Linear Equation 3. x + y = 0 4. 7z = 14

In an algebraic equation, the value of the expression on the left-hand side (LHS) is equal to the value
of the expression on the right-hand side (RHS) for a specific value of the variable. This specific
value of the variable, which makes the equation true, is known as the solution of the equation.

Consider the equation 3x + 7 = 19.
For x = 0 For x = 1 For x = –1 For x = 4

LHS = 3 × 0 + 7 = 7 LHS = 3 × 1 + 7 = 10 LHS = 3 × (–1) + 7 = 4 LHS = 3 × 4 + 7 = 19
RHS = 19 RHS = 19 RHS = 19 RHS = 19
∴ LHS  RHS ∴ LHS  RHS ∴ LHS  RHS ∴ LHS = RHS
The given equation is true when x = 4. Thus, x = 4 is the solution of the linear equation 3x + 7 = 19.

Example 1: Verify that x = 3 is the solution of the equation 4x – 1 = 11.
Solution: Substitute x = 3 in the given equation 4x – 1 = 11, we get

LHS = 4x – 1 = 4 × 3 – 1 = 12 – 1 = 11 and RHS = 11
Since, LHS = RHS

Therefore, x = 3 is the solution of the equation 4x – 1 = 11.

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