(x/2)+(x/4)+(x/8)=(x-(1/2)) variable domain {(5/7),(6/7),(4/8),(3/7),(2/7)
To solve the given equation: (x/2) + (x/4) + (x/8) = (x - 1/2), and find the values of the variable x from the given domain, follow these steps:
Step 1: Simplify the equation by finding a common denominator for the fraction terms on the left side of the equation.
- The common denominator for 2, 4, and 8 is 8.
- Rewrite each fraction with the common denominator:
(4x/8) + (2x/8) + (x/8) = (x - 1/2)
Step 2: Combine the like terms on the left side of the equation.
- Add the fractions: (4x + 2x + x)/8 = (x - 1/2)
- Simplify: (7x)/8 = (x - 1/2)
Step 3: Multiply both sides of the equation by 8 to clear the fraction.
- Multiply every term by 8: (8) * [(7x)/8] = (8) * [(x - 1/2)]
- Simplify: 7x = 8(x - 1/2)
- Distribute 8 to (x - 1/2): 7x = 8x - 4
Step 4: Move the variable terms to one side and the constant terms to the other side of the equation.
- Subtract 8x from both sides: 7x - 8x = -4
- Simplify: -x = -4
Step 5: Solve for x by dividing both sides of the equation by -1.
- Divide by -1: x = (-4) / (-1)
- Simplify: x = 4
So, from the given domain {(5/7), (6/7), (4/8), (3/7), (2/7)}, the value of the variable x that satisfies the equation is x = 4.