How do you solve #3(a + 2) + 5 = 2a + 4 #?

Question

Abigail Allen · Accepted Answer

The solutions is #a=-7#.

Use the distributive property to expand the parentheses, then isolate #a#: #3(a+2)+5=2a+4# #3a+6+5=2a+4# #3a+11=2a+4# #3a+11color(blue)-color(blue)11=2a+4color(blue)-color(blue)11# #3acolor(red)cancelcolor(Black)(color(black)+11color(blue)-color(blue)11)=2a+4color(blue)-color(blue)11# #3a=2a+4color(blue)-color(blue)11# #3a=2a-7# #3acolor(blue)-color(blue)(2a)=2a-7color(blue)-color(blue)(2a)# #3acolor(blue)-color(blue)(2a)=color(red)cancelcolor(black)(2a)-7color(red)cancelcolor(blue)(color(blue)-2a)# #3acolor(blue)-color(blue)(2a)=-7# #a=-7# I hope this was helpful. That's the solution.

Ethan Adkins · Answer

undefined To solve the equation 3(a + 2) + 5 = 2a + 4, follow these steps:

1. Distribute the 3 on the left side of the equation: 3(a + 2) = 3a + 6.
2. Combine like terms on the left side: 3a + 6 + 5 = 3a + 11.
3. Set the left side equal to the right side: 3a + 11 = 2a + 4.
4. Subtract 2a from both sides: 3a - 2a + 11 = 2a - 2a + 4, which simplifies to a + 11 = 4.
5. Subtract 11 from both sides: a + 11 - 11 = 4 - 11, which simplifies to a = -7.

Therefore, the solution to the equation 3(a + 2) + 5 = 2a + 4 is a = -7.