### 4.5 Phrases to Inequalities

Problem #

Problem Statement

Problems Similar To

1.

Write the inequality for: x is less than 10

\begin{equation}x\textrm{ }<\textrm{ }10\end{equation}

2.

Write the inequality for: x is greater than 4/4

\begin{equation}x\textrm{ }>\textrm{ }\frac{4}{4}\end{equation}

3.

Write the inequality for: 9 less than 8 times x is more than 31

\begin{equation}8x-9\textrm{ }>\textrm{ }31\end{equation}

4.

A weaver spends $\$400 $on supplies to make wall hangings and plans to sell the wall hangings for$ \$11$ 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}11w\textrm{ }>\textrm{ }400\end{equation}

5.

Mr. T needs at least 80 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{ }80\end{equation}

6.

Your scores in the first 3 tests are 66, 55 and 78. Write the reduced inequality for possible scores you can get on the last test and still have an average of at least 251/4.

\begin{equation}\frac{66+55+78+x}{4}\textrm{ }\ge\textrm{ }\frac{251}{4}\end{equation}

7.

You are in charge of buying the flowers for the flower beds around your school. You cannot spend over $\$112 $on flowers. The flowers cost$ \$14$ for a flat of flowers. Write the reduced inequality for the possible number of flats of flowers you can buy.

\begin{equation}14x\textrm{ }\le\textrm{ }112\end{equation}

8.

Peter wants to promote his band on the Internet. Site A offers website hosting for $\$3$per month and a startup fee of$\$66$. Site B offers website hosting for $\$81/5$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}3x+66\textrm{ }>\textrm{ }\frac{81}{5} \times x\end{equation} 9. Sania needs to read to atleast$69$pages of a book for homework. She has read$22$pages already. Write the reduced inequality for the number of pages she needs to read to complete her homework. \begin{equation}22+x\textrm{ }\ge\textrm{ }69\end{equation} 10. George has a strip of wood trim that is$ 33 $ft long. He needs$ 3 $ft pieces to trim some windows. Write the reduced inequality for the possible number of pieces he can cut. \begin{equation}3x\textrm{ }\le\textrm{ }33\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: 3x, x + 2 and 30?

\begin{equation}3x+x+2\textrm{ }>\textrm{ }30\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 + 9) and its width is 9.

\begin{equation}(x+9) \times 9\textrm{ }>\textrm{ }2(x+9+9)\end{equation}