Final answer:
The solution to the equation 5(2w+4)=4(2w+9) is obtained by expanding, collecting like terms, and solving for w, which results in w being equal to 8.
Step-by-step explanation:
The solution to the equation 5(2w+4)=4(2w+9) is found by expanding both sides and simplifying to isolate w. First, distribute the 5 and 4 on the left- and right-hand sides respectively:
- 5(2w) + 5(4) = 4(2w) + 4(9)
- 10w + 20 = 8w + 36
Then, collect like terms and solve for w:
- 10w - 8w = 36 - 20
- 2w = 16
- w = 8
So, the solution for w is 8.