%3D1%2F5(8-x).jpeg "1/4(x+1)=1/5(8-x)")
Solving the Equation 1/4(x+1) = 1/5(8-x)
In this article, we will solve the equation 1/4(x+1) = 1/5(8-x) and find the value of x.
Step 1: Simplify the Equation
To start, let's simplify the equation by multiplying both sides by 20, which is the least common multiple of 4 and 5.
1/4(x+1) = 1/5(8-x)
20[1/4(x+1)] = 20[1/5(8-x)]
This gives us:
5(x+1) = 4(8-x)
Step 2: Expand the Equations
Now, let's expand the equations:
5x + 5 = 32 - 4x
Step 3: Add 4x to Both Sides
Next, let's add 4x to both sides of the equation to get all the x terms on one side:
5x + 4x + 5 = 32
9x + 5 = 32
Step 4: Subtract 5 from Both Sides
Now, let's subtract 5 from both sides of the equation:
9x = 27
Step 5: Divide by 9
Finally, let's divide both sides of the equation by 9 to solve for x:
x = 27/9
x = 3
The Solution
Therefore, the value of x is 3.
We can verify our solution by plugging x = 3 back into the original equation:
1/4(3+1) = 1/5(8-3)
1/4(4) = 1/5(5)
1 = 1
As we can see, the equation is true when x = 3.
