Page 15 - Algebra 1

Solving a Linear Equation in One Variable
A polynomial equation in one variable is when two algebraic expressions are set equal. For example,
5x + 4 = 9
REMEMBER:
• As per the addition principle of equality, the same number can be subtracted or added on both sides of the equation. When you use the same number on both sides, the equality is maintained. Forexample, 2x+1=3
or 2x + 1 + 2 = 3 + 2
2x + 3 = 5
• As per the multiplication principle of equality, the same number can be multiplied or divided on both sides of the equation. When you use the same number on both sides, the equality is maintained.
For example,
3x = 5
5 (3x) = 5 (5) 15x = 25
• When transposing number or variables from LHS to RHS or RHS to LHS, change the sign from +ve to –ve and –ve to +ve.
Worked Example 6
Find the solution of 5x – 4 = 11
Solution:
Add 4 on both sides
x =3
5x – 4 + 4 = 11 + 4
5x = 15
Worked Example 7
The sum of the two numbers is 84. If one of the numbers is 12 more than the other, find the two
numbers.
Solution:
Let the first number be x
The second number be x + 12
Sum of numbers = 84
x + x + 12 = 84
2x = 84 – 12
2x = 72
x = 36
Second number = x + 12 = 36 + 12 = 48
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ALGEBRA