SOLUTION: What Is the value of n that satisfies the equation below -5(2n+3)+3(3n+4)= -8

Question 1099191: What Is the value of n that satisfies the equation below
-5(2n+3)+3(3n+4)= -8
Found 2 solutions by math_helper, ikleyn:
Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!
What Is the value of n that satisfies the equation below
-5(2n+3)+3(3n+4)= -8
=======================================
The process is called "solving for n" (you will see "solving for x" a lot in Algebra, the letter is merely a placeholder). What we want is n by itself ("one n") on one side of the equation and some number on the other side.
�
First, distribute (multiply within parenthesis) the -5 and we will also distribute the 3 into its parenthesis as well:
(-10n - 15) + (9n + 12) = -8
�
Re-writing without parenthesis:
-10n -15 + 9n +12 = -8
[ side note: when removing parenthesis, if you have something like " - (a + b - c)" the signs will all change when you remove the parenthesis, so you'd write: " -a - b + c ". ]
�
Now collect like-terms (this just means adding the coefficients of "n" terms, and adding the constants� but in the future you will see things like or � just remember collecting like-terms applies similarly):
-n - 3 = -8
�
Now, since we have all negative terms, we can multiply both sides by -1:
(-1)(-n - 3) = (-1)(-8)
n + 3 = 8 (as long as you do the same operation to both sides, the equality is retained)

�
Finally, just subtract 3 from each side:
n + 3 - 3 = 8 - 3
n + 0 = 5
ANS: n = 5
�
Check:
To do the check, we plug in n=5 in the original equation and check that both sides are equal. Here we can work just with the left side and note that the computation should give us -8:
-5 (2(5)+3)+3(3(5) + 4) = -5(13) + (3(19)) = -65 + 57 = -8 (ok)

Answer by ikleyn(52783)   (Show Source): You can put this solution on YOUR website!
.
Also, on solving single linear equation see the lesson
    - HOW TO solve a linear equation
in this site.

RELATED QUESTIONS
Please help with this questions, prove by induction that the formulas positive integral... (answered by ikleyn)
What are the steps in solving this equation?... (answered by richwmiller)
What value of m satisfies the equation shown below? 5(m - 5) = 3(m + 1) (answered by checkley79)
what is 2n+2n =... (answered by ikleyn)
What is the sum of {{{ sum( (3 * 5^(n+1)/2^(2n)), n=8, 13)... (answered by greenestamps,Edwin McCravy)
What is the difference in simplest form? n^2+3n+2/n^2+6b+8 -... (answered by jsmallt9)
Use the method of mathematical induction to establish the following 1.... (answered by ikleyn)
What is the complete factorization of -n^4-3n^2-2n (answered by Edwin McCravy)
Perform the indicated operation h(n)=2n-3 g(n)=3n-4 Find (h o... (answered by Ave,MathTherapy)