The value of x that satisfies the equation 2/3x + 4 = 3/2(x-4) is?
Answers
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:
Final answer:
The value of x that satisfies the equation 2/3x + 4 = 3/2(x-4) is 8.4
Explanation:
To find the value of x that satisfies the equation 2/3x + 4 = 3/2(x-4), we first distribute 3/2 into the parenthesis to get 2/3x + 4 = 3/2x - 3/2. Now isolate x on one side of the equation. To eliminate fractions, multiply all terms by 6 giving 4x + 24 = 9x - 18. Rearrange the terms to form a linear equation 5x = 42, hence x = 42 / 5 = 8.4 is the solution to the equation.
Learn more about Equation Solving here:
#SPJ11
Related Questions
The Slope of a Line(8,2) and (5,11)Calculate the slope of the linethat contains the given points.
What is the difference between -0.4 and 44.4?
Covert 3/8, 2/9, 4/7, and 1/5 to decimal
Help please! Which term means to do away with something?A. temperance B. abolition C. labor boycott D. civil disobedience
Choose all answers that apply:
(Choice A)
A
P=5P=5P, equals, 5 and Q=12Q=12Q, equals, 12
(Choice B)
B
P=-5P=−5P, equals, minus, 5 and Q=-12Q=−12Q, equals, minus, 12
(Choice C)
C
P=5P=5P, equals, 5 and Q=-5Q=−5Q, equals, minus, 5
(Choice D)
D
P=-12P=−12P, equals, minus, 12 and Q=-12Q=−12
Answers
Answer:
Option A, C and D are correction Option.
Step-by-step explanation:
Given Equation, -5x + 12 = Px + Q
We have to value of P and Q from given options such that equation has exactly one solution.
First simplify the equation,
-5x + 12 = Px + Q
-5x - Px = Q - 12
(-5 - P)x = Q - 12
from above P can not have value equal to -5 as if P = -5
we have (-5 - (-5))x = Q - 12
(-5 + 5)x = Q - 12
this equation has infinitely many solution as it removes x from the equation.
So, Option B is not our solution other than that All Options are our solution.
A).
P = 5 & Q = 12
⇒ (-5 - 5)x = 12 - 12
x = 0
C).
P = 5 & Q = -5
⇒ (-5 - 5)x = -5 - 12
-10x = -17
D).
P = -12 & Q = -12
⇒ (-5 - (-12))x = -12 - 12
7x = -24
Therefore, Option A, C and D are correction Option.
We are given equation : -5x+12=Px+Q.
Let us compare left and right sides of the equation.
On comparing Px = -5x.
Dividing both sides by x, we get
Px/x = -5x/x.
P = -5.
Let us compare other part of the given equation.
Q =12.
Therefore, we got P=-5 and Q =12.
Non of the given options seems correct.
Please check the option have P=-5 and Q =12.
Answers
Volume = 57.5 cm x 52.5cm x 29.5cm
Volume = 89053.1252 cm^3
B. 3151 m^2
C. 2548 m^2
Answers
Answers
If you are graphing on a number line, then you would plot an open circle at 4 and shade to the left of the open circle. The open circle tells the reader "do not include this point as part of the solution set". The shaded region is the solution set.
If you are graphing on the xy coordinate axis system, then you'll graph a vertical line through 4 on the x axis. This vertical line is made to be dotted or dashed to tell the reader not to include any point on the vertical line. Shade to the left of this vertical dashed/dotted line to represent the set of all solution points. These points will have x coordinates less than 4. The y coordinate can be any point you want. Eg: (3,5) and (2,7) are two such solutions.
Answers
10. 25 is what percent of 125?