Final answer:
To solve the equation 3(4+5x)/5−2(5x−2)/3=2, we can begin by simplifying the equation using the distributive property and combining like terms. Then, we can eliminate the fractions by multiplying every term by the least common multiple of the denominators. Next, we can find a common denominator and combine like terms. Finally, we solve for x by moving terms around and dividing both sides of the equation. Thus the value of x is = -242/115
Step-by-step explanation:
To solve the equation 3(4+5x)/5−2(5x−2)/3=2, we can begin by simplifying the equation using the distributive property and combining like terms:
Multiply 3 and 4+5x to get 12+15x
Multiply 2 and 5x-2 to get 10x-4
Now, we can rewrite the equation as (12+15x)/5 - (10x-4)/3 = 2. To eliminate the fractions, we can multiply every term in the equation by the least common multiple of the denominators, which is 15:
Multiply (12+15x)/5 by 3 to get (36+45x)/5
Multiply (10x-4)/3 by 5 to get (50x-20)/3
Now our equation becomes (36+45x)/5 - (50x-20)/3 = 30. To simplify further, we can find a common denominator and combine like terms:
Combine (36+45x)/5 and (50x-20)/3 using the common denominator of 15:
(3(36+45x) - 5(50x-20))/15 = 30
Distribute 3 and 5 to simplify the numerator:
(108+135x - 250x + 100)/15 = 30
Combine like terms in the numerator:
(208-115x)/15 = 30
Multiply both sides of the equation by 15 to eliminate the fraction:
208-115x = 450
Finally, solve for x by moving the terms around:
-115x = 242
Divide both sides by -115:
x = -242/115