Solving the Equation: 1/2x - 4/5 = 1/5x - 16/5 + 1/10x
In this article, we will solve the equation 1/2x - 4/5 = 1/5x - 16/5 + 1/10x step by step.
Step 1: Simplify the Equation
First, let's simplify the equation by combining like terms:
1/2x - 4/5 = 1/5x - 16/5 + 1/10x
Combine the fractions on the right-hand side:
1/2x - 4/5 = (1/5x + 1/10x) - 16/5
Simplify the right-hand side:
1/2x - 4/5 = (3/10)x - 16/5
Step 2: Isolate x
Now, let's isolate x by adding 4/5 to both sides of the equation:
1/2x = (3/10)x - 16/5 + 4/5
Simplify the right-hand side:
1/2x = (3/10)x - 12/5 + 4/5
Combine the fractions:
1/2x = (3/10)x - 8/5
Step 3: Solve for x
Now, let's solve for x by subtracting (3/10)x from both sides of the equation:
(1/2 - 3/10)x = -8/5
Simplify the left-hand side:
(2/10)x = -8/5
Divide both sides by 2/10:
x = -8/5 * 10/2
Simplify:
x = -16/5
Therefore, the value of x is -16/5.
