To solve the equation (3x/5) + (3x/4) - (3/2) = (4/5) - x, follow these steps:
Step 1: Find a common denominator for the fractions on the left side of the equation. In this case, the common denominator is 20.
So, rewrite the equation with a common denominator:
(12x/20) + (15x/20) - (30/20) = (4/5) - x
Step 2: Combine like terms on both sides of the equation. On the left side, add the fractions:
(12x/20 + 15x/20) - (30/20) = (4/5) - x
(27x/20) - (30/20) = (4/5) - x
Step 3: Simplify further by adding the fractions and combining like terms:
(27x - 30)/20 = (4/5) - x
Step 4: To get rid of the fraction on the right side, multiply both sides of the equation by 20 (the denominator on the left side):
20 * ((27x - 30)/20) = 20 * ((4/5) - x)
This simplifies to:
27x - 30 = (80/5) - 20x
Step 5: Continue to simplify:
27x - 30 = 16 - 20x
Step 6: Add 20x to both sides of the equation to isolate the x terms on one side:
27x + 20x - 30 = 16
Combine like terms:
47x - 30 = 16
Step 7: Add 30 to both sides to isolate the x term:
47x - 30 + 30 = 16 + 30
This simplifies to:
47x = 46
Step 8: Finally, divide both sides by 47 to solve for x:
(47x)/47 = 46/47
x = 46/47
So, the solution to the equation is x = 46/47.