How do you solve 19a - 3(a - 6) = 66 for a?

2 Answers
Jun 12, 2017

See a solution process below:

Explanation:

First expand the term in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:

19a - color(red)(3)(a - 6) = 66

19a - (color(red)(3) * a) + (color(red)(3) * 6) = 66

19a - 3a + 18 = 66

Next, combine like terms:

(19 - 3)a + 18 = 66

16a + 18 = 66

Then, subtract color(red)(18) from each side of the equation to isolate the a term while keeping the equation balanced:

16a + 18 - color(red)(18) = 66 - color(red)(18)

16a + 0 = 48

16a = 48

Now, divide each side of the equation by color(red)(16) to solve for a while keeping the equation balanced:

(16a)/color(red)(16) = 48/color(red)(16)

(color(red)(cancel(color(black)(16)))a)/cancel(color(red)(16)) = 3

a = 3

Jun 12, 2017

a = 3

Explanation:

19a - 3(a-6) = 66

19a - 3a + 18 = 66

19a - 3a color(red)(cancel(color(black)(+ 18) - 18)) = 66 color(red)(- 18)

19a - 3a = 66 - 18

16a = 66 - 18

16a = 48

color(red)(cancel(color(black)(16))) a color(red)(cancel(÷ 16)) = 48 ÷ 16

a = 48 ÷ 16

color(blue)(a = 3

We can substitute a for 3 to prove our answer.

19 xx 3 - 3(3 - 6) = 66

19 xx 3 - 3 xx -3 = 66

57 - 3 xx -3 = 66

57 - -9 = 66

57 + 9 = 66