Question

set on a number line.Solve each inequality. Describe the solution set using set builder or interval notation. Then graph the solution

63. $\mathbf{3}\mathbf{n}\mathbf{+}\mathbf{4}\left(\mathbf{n}\mathbf{+}\mathbf{3}\right)<\mathbf{5}\left(\mathbf{n}\mathbf{+}\mathbf{2}\right)$

Short answer

Solution set of inequality is $\mathbf{(}\mathbf{-}\infty \mathbf{,}\mathbf{-}\mathbf{1}\mathbf{)}$.

Solution set on number line is

Step-by-step solution

- Write properties of inequality.

Properties of inequalities are written in following table:

- Solve 3n+4n+3<5n+2.

To solve given inequality, use subtraction and division properties of inequality. To solve given inequality, expand the parentheses on each side. Subtract 12 from each side then subtract $5n$from each side and then divide each side of the inequality by 2

$\begin{array}{l}3n+4n+12<5n+10\\ 7n+12-12<5n+10-12\\ 7n-5n<5n-2-5n\\ \frac{2n}{2}<\frac{-2}{2}\\ n<-1\end{array}$

Thus, solution is $n<-1$.

– Describe solution set in interval notation.

Assolution set of the inequality is all real numbers less than $-1$.

Write the solution set in interval notation.

$(-\infty ,-1)$

– Graph the solution set

Open circle on $-1$shows this point is excluded in the solution set