Question

solve the linear inequality for n. graph your answer in the number line. then write the solution in inequality notation.
-64 > -4n + 2(8n - 8)
show your work here
hint: to add inequalities (<, >, ≤, ≥), type \less\ or \greater\

Explanation:

Step1: Expand the right - hand side

First, expand $2(8n - 8)$ using the distributive property $a(b - c)=ab - ac$. So, $2(8n - 8)=16n-16$. The inequality becomes $-64>-4n + 16n-16$.

Step2: Combine like terms

Combine the $n$ terms on the right - hand side: $-4n+16n = 12n$. The inequality is now $-64>12n-16$.

Step3: Add 16 to both sides

To isolate the term with $n$, add 16 to both sides of the inequality. $-64 + 16>12n-16 + 16$, which simplifies to $-48>12n$.

Step4: Divide both sides by 12

Divide both sides of the inequality $-48>12n$ by 12. Since we are dividing by a positive number, the direction of the inequality sign remains the same. $\frac{-48}{12}>\frac{12n}{12}$, so $-4>n$ or $n < - 4$.

Answer:

The solution in inequality notation is $n < - 4$. On the number line, we have an open circle at - 4 (because the inequality is strict, $n
eq - 4$) and the line extends to the left of - 4.