How do you solve #7(5a-4)-1=14-8a#?

Question

Hazel Anglin · Accepted Answer

See the entire solution process below:

First, expand the term in parenthesis on the left side of the equation by multiplying each term within the parenthesis by #color(red)(7)#: #(color(red)(7) xx 5a) - (color(red)(7) xx 4) - 1 = 14 - 8a# #35a - 28 - 1 = 14 - 8a# #35a - 29 = 14 - 8a# Next, add #color(red)(29)# and #color(blue)(8a)# to each side of the equation to isolate the #a# term while keeping the equation balanced: #35a - 29 + color(red)(29) + color(blue)(8a) = 14 - 8a + color(red)(29) + color(blue)(8a)# #35a + color(blue)(8a) - 29 + color(red)(29) = 14 + color(red)(29) - 8a + color(blue)(8a)# #43a - 0 = 43 - 0# #43a = 43# Now, divide each side of the equation by #color(red)(43)# to solve for #a# while keeping the equation balanced: #(43a)/color(red)(43) = 43/color(red)(43)# #(color(red)(cancel(color(black)(43)))a)/cancel(color(red)(43)) = 1# #a = 1#

Eli Assouline · Answer

undefined To solve the equation 7(5a-4)-1=14-8a, follow these steps:

1. Distribute the 7 to the terms inside the parentheses: 35a - 28 - 1 = 14 - 8a.
2. Combine like terms: 35a - 29 = 14 - 8a.
3. Add 8a to both sides to isolate the variable terms on one side of the equation: 35a + 8a - 29 = 14.
4. Combine like terms: 43a - 29 = 14.
5. Add 29 to both sides to isolate the variable term: 43a = 43.
6. Divide both sides by 43 to solve for a: a = 1.