Question

date:
question 4 is a
ork!
5(2 - 11n) + 4 = 51 - 10n
10 - 55n + 4 = 51 - 10n
14 - 55n = 51 - 10n
+10n +10n
14 - 45n = 51
-14 -14
-45n = 37
-45 -45
n =...
-5x - 4(5x - 10) > 40 - 2x

Explanation:

Step1: Expand the left - hand side

We start with the equation \(5(2 - 11n)+4 = 51-10n\). Using the distributive property \(a(b + c)=ab+ac\), we expand \(5(2 - 11n)\) to get \(10-55n\). So the equation becomes \(10 - 55n+4=51 - 10n\).

Step2: Combine like terms on the left - hand side

Combine the constant terms \(10\) and \(4\) on the left - hand side. \(10 + 4=14\), so the equation is now \(14-55n=51 - 10n\).

Step3: Add \(55n\) to both sides

To get all the \(n\) terms on one side, we add \(55n\) to both sides of the equation. \((14-55n)+55n=(51 - 10n)+55n\), which simplifies to \(14 = 51+45n\).

Step4: Subtract 51 from both sides

Subtract \(51\) from both sides: \(14-51=51 + 45n-51\). Calculating \(14 - 51=-37\), so we have \(-37 = 45n\).

Step5: Solve for \(n\)

Divide both sides by \(45\): \(n=\frac{-37}{45}\)

Answer:

\(n =-\frac{37}{45}\)