%3D-1%2F4(x-4)%2B7.jpeg "1/2(x-5)=-1/4(x-4)+7")
Solving the Equation: 1/2(x-5)=-1/4(x-4)+7
In this article, we will solve the equation 1/2(x-5)=-1/4(x-4)+7 using basic algebraic operations.
Step 1: Multiply both sides by the least common multiple (LCM) of 2 and 4, which is 4.
To eliminate the fractions, we multiply both sides of the equation by 4, which gives us:
2(x-5) = -(x-4)+28
Step 2: Expand the left-hand side of the equation.
Expanding the left-hand side, we get:
2x - 10 = -(x-4)+28
Step 3: Expand the right-hand side of the equation.
Expanding the right-hand side, we get:
2x - 10 = -x + 4 + 28
Step 4: Simplify the equation.
Simplifying the equation, we get:
2x - 10 = -x + 32
Step 5: Add x to both sides of the equation.
Adding x to both sides, we get:
3x - 10 = 32
Step 6: Add 10 to both sides of the equation.
Adding 10 to both sides, we get:
3x = 42
Step 7: Divide both sides of the equation by 3.
Dividing both sides by 3, we get:
x = 14
Therefore, the value of x is 14.
By following these steps, we have successfully solved the equation 1/2(x-5)=-1/4(x-4)+7 and found the value of x.
