How do you solve #10 / (2x+6) + 2 / (x+3) = 1/2#?

Question

Avery Alexander · Accepted Answer

Using the lowest common denominator. #2x + 6# is the very same double of #x+3#. So, the lowest common denominator between the two fractions is #2x+6# itself. Summing both, we'd have #(10+4)/(2x+6) = 1/2# Multiplying in cross, we'd have #1*(2x+6) = 2*(10+4)# #2x + 6 = 28#
#2x = 22#
#x = 11# :)

Julia Adams · Answer

undefined To solve the equation 10 / (2x+6) + 2 / (x+3) = 1/2, you can follow these steps:

1. Find a common denominator for the fractions on the left side of the equation. In this case, the common denominator is (2x+6)(x+3).

2. Multiply each term by the common denominator to eliminate the fractions. This will give you: 10(x+3) + 2(2x+6) = (1/2)(2x+6)(x+3).

3. Simplify both sides of the equation by distributing and combining like terms. This will result in: 10x + 30 + 4x + 12 = (x+3)(x+6).

4. Continue simplifying the equation by combining like terms: 14x + 42 = x^2 + 9x + 18.

5. Rearrange the equation to bring all terms to one side: x^2 - 5x - 24 = 0.

6. Factor the quadratic equation: (x - 8)(x + 3) = 0.

7. Set each factor equal to zero and solve for x: x - 8 = 0 or x + 3 = 0.

8. Solve for x in each equation: x = 8 or x = -3.

Therefore, the solutions to the equation 10 / (2x+6) + 2 / (x+3) = 1/2 are x = 8 and x = -3.