Question

Solve the following inequality for n. Write your answer in the simplest form.9n + 4 ≤ 6n - 6

Answer 1

Given,

The expression is,

$9n+4\le6n-6$

Substracting 4 from both sides then,

$\begin{gathered} 9n+4-4\le6n-6-4 \\ 9n\le6n-10 \end{gathered}$

Substracting 6n from both sides then,

$\begin{gathered} 9n\le6n-10 \\ 9n-6n\le6n-6n-10 \\ 3n\le-10 \end{gathered}$

Multiplying both sides by 1/3 then,

$\begin{gathered} 3n\le-10 \\ 3n\times\frac{1}{3}\le-10\times\frac{1}{3} \\ n\le-\frac{10}{3} \end{gathered}$

Hence, the solution for n is n<= (-10/3).