Given that: 4(2g + 104) - 96 = 504 + 6(g - 14), solve for g.
i'm confused on how to set this problem up - if anyone could help that would be great. thank you.
expand first
4(2g + 104) - 96 = 504 + 6(g - 14)
8g + 416 - 96 = 504 + 6g - 84
collect like terms and simplify
8g + 320 = 6g + 420
terms on one side, constants on the other side
8g - 6g = 420 -320
2g = 100
g = 50
never mind, i figured it out! :)
g= 50
To solve the equation 4(2g + 104) - 96 = 504 + 6(g - 14) for the variable g, you need to simplify both sides of the equation and isolate the term containing g. Here's a step-by-step breakdown of how to set up and solve the problem:
1. Distribute the 4 to the terms inside the parentheses on the left side of the equation:
8g + 416 - 96 = 504 + 6(g - 14)
Simplify: 8g + 320 = 504 + 6(g - 14)
2. Distribute the 6 to the terms inside the parentheses on the right side of the equation:
8g + 320 = 504 + 6g - 84
Simplify: 8g + 320 = 6g + 420
3. Combine like terms on both sides of the equation:
Subtract 6g from both sides: 8g - 6g + 320 = 6g - 6g + 420
Simplify: 2g + 320 = 420
4. To isolate the term containing g, subtract 320 from both sides of the equation:
2g + 320 - 320 = 420 - 320
Simplify: 2g = 100
5. Finally, divide both sides of the equation by 2 to solve for g:
(2g) / 2 = 100 / 2
Simplify: g = 50
Therefore, the solution to the equation is g = 50.