Algebra-1 Problems

4.5 Phrases to Inequalities


Problem #

Problem Statement

Problems Similar To

1.

Write the inequality for: x is less than 8

\begin{equation}x\textrm{ }<\textrm{ }8\end{equation}

2.

Write the inequality for: x is greater than 2/7

\begin{equation}x\textrm{ }>\textrm{ }\frac{2}{7}\end{equation}

3.

Write the inequality for: 5 less than 8 times x is more than 51

\begin{equation}8x-5\textrm{ }>\textrm{ }51\end{equation}

4.

A weaver spends $ \$224 $ on supplies to make wall hangings and plans to sell the wall hangings for $ \$18 $ 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}18w\textrm{ }>\textrm{ }224\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 70, 90 and 78. Write the reduced inequality for possible scores you can get on the last test and still have an average of at least 147/2.

\begin{equation}\frac{70+90+78+x}{4}\textrm{ }\ge\textrm{ }\frac{147}{2}\end{equation}

7.

You are in charge of buying the flowers for the flower beds around your school. You cannot spend over $ \$132 $ 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{ }132\end{equation}

8.

Peter wants to promote his band on the Internet. Site A offers website hosting for $\$5$ per month and a startup fee of $\$55$. Site B offers website hosting for $\$75/4$ 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}5x+55\textrm{ }>\textrm{ }\frac{75}{4} \times x\end{equation}

9.

Sania needs to read to atleast $125$ pages of a book for homework. She has read $78$ pages already. Write the reduced inequality for the number of pages she needs to read to complete her homework.

\begin{equation}78+x\textrm{ }\ge\textrm{ }125\end{equation}

10.

George has a strip of wood trim that is $ 18 $ 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{ }18\end{equation}

11.

At an online bookstore, Sandra bought $9$ copies of the same book for the members of her book club. She got free shipping because the total price was at least $\$171$. Write the reduced inequality for the price of each book.

\begin{equation}9x\textrm{ }\ge\textrm{ }171\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 + 3 and 53?

\begin{equation}9x+x+3\textrm{ }>\textrm{ }53\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 + 6) and its width is 13.

\begin{equation}(x+6) \times 13\textrm{ }>\textrm{ }2(x+6+13)\end{equation}