Algebra-1 Problems

4.5 Phrases to Inequalities


Problem #

Problem Statement

Problems Similar To

1.

Write the inequality for: x is less than 9

\begin{equation}x\textrm{ }<\textrm{ }9\end{equation}

2.

Write the inequality for: x is greater than 9/10

\begin{equation}x\textrm{ }>\textrm{ }\frac{9}{10}\end{equation}

3.

Write the inequality for: 2 less than 6 times x is more than 40

\begin{equation}6x-2\textrm{ }>\textrm{ }40\end{equation}

4.

A weaver spends $ \$244 $ on supplies to make wall hangings and plans to sell the wall hangings for $ \$23 $ 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}23w\textrm{ }>\textrm{ }244\end{equation}

5.

Mr. T needs at least 60 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{ }60\end{equation}

6.

Your scores in the first 3 tests are 97, 94 and 62. Write the reduced inequality for possible scores you can get on the last test and still have an average of at least 331/4.

\begin{equation}\frac{97+94+62+x}{4}\textrm{ }\ge\textrm{ }\frac{331}{4}\end{equation}

7.

You are in charge of buying the flowers for the flower beds around your school. You cannot spend over $ \$247 $ on flowers. The flowers cost $ \$19 $ for a flat of flowers. Write the reduced inequality for the possible number of flats of flowers you can buy.

\begin{equation}19x\textrm{ }\le\textrm{ }247\end{equation}

8.

Peter wants to promote his band on the Internet. Site A offers website hosting for $\$9$ per month and a startup fee of $\$72$. Site B offers website hosting for $\$45$ 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}9x+72\textrm{ }>\textrm{ }45x\end{equation}

9.

Sania needs to read to atleast $78$ pages of a book for homework. She has read $38$ pages already. Write the reduced inequality for the number of pages she needs to read to complete her homework.

\begin{equation}38+x\textrm{ }\ge\textrm{ }78\end{equation}

10.

George has a strip of wood trim that is $ 54 $ ft long. He needs $ 6 $ ft pieces to trim some windows. Write the reduced inequality for the possible number of pieces he can cut.

\begin{equation}6x\textrm{ }\le\textrm{ }54\end{equation}

11.

At an online bookstore, Sandra bought $11$ copies of the same book for the members of her book club. She got free shipping because the total price was at least $\$154$. Write the reduced inequality for the price of each book.

\begin{equation}11x\textrm{ }\ge\textrm{ }154\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: 9x, x + 6 and 86?

\begin{equation}9x+x+6\textrm{ }>\textrm{ }86\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 + 7) and its width is 9.

\begin{equation}(x+7) \times 9\textrm{ }>\textrm{ }2(x+7+9)\end{equation}