Final answer:
To solve the equation 2/3x + 8/15 = 52/10 for x, multiply both sides of the equation by the least common denominator (LCD) of the fractions and isolate the variable x. After simplifying and solving, we find that x = 7.
Step-by-step explanation:
To solve the equation 2/3x + 8/15 = 52/10 for x, we need to isolate the variable x.
First, let's get rid of the fractions by multiplying every term in the equation by the least common denominator (LCD) of all the fractions involved, which is 30. Multiplying both sides of the equation by 30 gives us:
30 * (2/3x) + 30 * (8/15) = 30 * (52/10)
Simplifying, we get:
20x + 16 = 156
Next, subtract 16 from both sides of the equation:
20x = 156 - 16
20x = 140
To solve for x, divide both sides of the equation by 20:
x = 140/20
Simplifying, we find that x = 7.