Answer:
A solution to an equation is a value of a variable that makes the equation true. From the statement "Which value of x satisfies the equation", we need to understand that, we have to find the value of x from the given question.
Let us see some example problems based on the above concept.
Example 1 :
Which value of x is the solution of the equation
(2/3) x + (1/2) = (5/6) ?
Solution :
(2/3) x + (1/2) = (5/6)
(2x/3) + (1/2) = (5/6)
(4x + 3)/6 = (5/6)
Multiply 6 on both sides
4x + 3 = 5
Subtract 3 on both sides
4x + 3 - 3 = 5 - 3
4x = 2
Divide by 4 on both sides
4x/4 = 2/4
x = 1/2
Hence the value 1/2 will satisfy the above equation.
Example 2 :
Which value of x is the solution of the equation
(2/3) x + (x/6) = 5 ?
Solution :
(2x/3) + (x/6) = 5
(4x/6) + (x/6) = 5
(4x + x)/6 = 5
5x/6 = 5
Multiply by 6 on both sides
5x = 5 (6)
5x = 30
Divide by 5 on both sides
x = 30/5 = 6
Hence the value 6 will satisfy the above equation.
Example 3 :
The number of people on the school board is represented by x. Two subcommittees with an equal number of members are formed, one with (2x/3) − 5 members and the other with x/4 members. How many people are on the school board?
Solution :
From the above question, we come to know that we have to solve for x, that makes the statement true.
(2x/3) − 5 = x/4
(2x - 15)/3 = x/4
Multiply 3 on both sides
2x - 15 = 3x/4
Multiply by 4 on both sides
4(2x - 15) = 3x
8x - 60 = 3x
Subtract 3x on both sides
8x - 3x - 60 = 0
5x - 60 = 0
Add by 60 on both sides
5x - 60 + 60 = 0 + 60
5x = 60
Divide by 5 on both sides
x = 60/5
x = 12
Example 4 :
What is the value of x in the equation
(x − 2)/3 + 1/6 = 5/6 ?
Solution :
(x − 2)/3 + 1/6 = 5/6
(2(x - 2) + 1)/6 = 5/6
multiply by 6 on both sides
(2x - 4 + 1) = 5
2x - 3 = 5
Add 3 on both sides
2x - 3 + 3 = 5 + 3
2x = 8
Divide by 2 on both sides
x = 8/2
x = 4
Step-by-step explanation:
