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

Question

8728 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-27T15:00:15

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:

$(43a)/color(red)(43) = 43/color(red)(43)$

$(color(red)(cancel(color(black)(43)))a)/cancel(color(red)(43)) = 1$

$a = 1$

How do you solve 7(5a-4)-1=14-8a7(5a-4)-1=14-8a?