### 4.5 Phrases to Inequalities

Problem #

Problem Statement

Problems Similar To

1.

Write the inequality for: x is less than 4

\begin{equation}x\textrm{ }<\textrm{ }4\end{equation}

2.

Write the inequality for: x is greater than 9/8

\begin{equation}x\textrm{ }>\textrm{ }\frac{9}{8}\end{equation}

3.

Write the inequality for: 6 less than 11 times x is more than 93

\begin{equation}11x-6\textrm{ }>\textrm{ }93\end{equation}

4.

A weaver spends $\$300 $on supplies to make wall hangings and plans to sell the wall hangings for$ \$21$ each. Write an inequality that gives the possible number 'w' of wall hangings that the weaver needs to sell in order to be profitable.

\begin{equation}21w\textrm{ }>\textrm{ }300\end{equation}

5.

Mr. T needs at least 90 milligrams of vitamin C each day. He gets his vitamin C by munching brussel sprouts. Each sprout furnishes 10 milligrams of vitamin C. Write the reduced inequality that gives the number of sprouts (x) he must eat each day.

\begin{equation}10x\textrm{ }\ge\textrm{ }90\end{equation}

6.

Your scores in the first 3 tests are 62, 71 and 61. Write the reduced inequality for possible scores you can get on the last test and still have an average of at least 293/4.

\begin{equation}\frac{62+71+61+x}{4}\textrm{ }\ge\textrm{ }\frac{293}{4}\end{equation}

7.

You are in charge of buying the flowers for the flower beds around your school. You cannot spend over $\$48 $on flowers. The flowers cost$ \$12$ for a flat of flowers. Write the reduced inequality for the possible number of flats of flowers you can buy.

\begin{equation}12x\textrm{ }\le\textrm{ }48\end{equation}

8.

Peter wants to promote his band on the Internet. Site A offers website hosting for $\$7$per month and a startup fee of$\$21$. Site B offers website hosting for $\$77/8$per month with no startup fee. Write the reduced inequality for the number of months Peter would need to keep the website with Site B to be less expensive than with Site A? \begin{equation}7x+21\textrm{ }>\textrm{ }\frac{77}{8} \times x\end{equation} 9. Sania needs to read to atleast$121$pages of a book for homework. She has read$72$pages already. Write the reduced inequality for the number of pages she needs to read to complete her homework. \begin{equation}72+x\textrm{ }\ge\textrm{ }121\end{equation} 10. George has a strip of wood trim that is$ 63 $ft long. He needs$ 9 $ft pieces to trim some windows. Write the reduced inequality for the possible number of pieces he can cut. \begin{equation}9x\textrm{ }\le\textrm{ }63\end{equation} 11. At an online bookstore, Sandra bought$7$copies of the same book for the members of her book club. She got free shipping because the total price was at least$\$84$. Write the reduced inequality for the price of each book.

\begin{equation}7x\textrm{ }\ge\textrm{ }84\end{equation}

12.

The sum of the lengths of any two sides of a triangle should be greater than the length of the third side. Write the reduced inequality for possible values of "x" for a triangle with sides: 4x, x + 8 and 23?

\begin{equation}4x+x+8\textrm{ }>\textrm{ }23\end{equation}

13.

Write the reduced inequality for values of "x" if the area of a rectangle is greater than its perimeter, and if the length of the rectangle is (x + 11) and its width is 8.

\begin{equation}(x+11) \times 8\textrm{ }>\textrm{ }2(x+11+8)\end{equation}