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Solve the equation
3x/5 + 3x/4 - 3/2 = 4/5 - x

2 Answers

1 vote

Explanation:

Multiply everything in the equation by 20 ( this is the Lowest Common denominator of 5 4 and 2) to get :

12x + 15x - 30 = 16 - 20 x

47x = 46

x = 46/47

User Chirag Bhansali
by
7.5k points
2 votes
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.
User Miotsu
by
8.0k points

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