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 10/2

\begin{equation}x\textrm{ }>\textrm{ }\frac{10}{2}\end{equation}

3.

Write the inequality for: 7 less than 11 times x is more than 15

\begin{equation}11x-7\textrm{ }>\textrm{ }15\end{equation}

4.

A weaver spends $ \$700 $ on supplies to make wall hangings and plans to sell the wall hangings for $ \$16 $ 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}16w\textrm{ }>\textrm{ }700\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 65, 93 and 81. Write the reduced inequality for possible scores you can get on the last test and still have an average of at least 153/2.

\begin{equation}\frac{65+93+81+x}{4}\textrm{ }\ge\textrm{ }\frac{153}{2}\end{equation}

7.

You are in charge of buying the flowers for the flower beds around your school. You cannot spend over $ \$154 $ 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{ }154\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 $\$87$. Site B offers website hosting for $\$56/3$ 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+87\textrm{ }>\textrm{ }\frac{56}{3} \times x\end{equation}

9.

Sania needs to read to atleast $120$ pages of a book for homework. She has read $91$ pages already. Write the reduced inequality for the number of pages she needs to read to complete her homework.

\begin{equation}91+x\textrm{ }\ge\textrm{ }120\end{equation}

10.

George has a strip of wood trim that is $ 40 $ ft long. He needs $ 8 $ ft pieces to trim some windows. Write the reduced inequality for the possible number of pieces he can cut.

\begin{equation}8x\textrm{ }\le\textrm{ }40\end{equation}

11.

At an online bookstore, Sandra bought $5$ copies of the same book for the members of her book club. She got free shipping because the total price was at least $\$90$. Write the reduced inequality for the price of each book.

\begin{equation}5x\textrm{ }\ge\textrm{ }90\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: 6x, x + 6 and 55?

\begin{equation}6x+x+6\textrm{ }>\textrm{ }55\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 11.

\begin{equation}(x+6) \times 11\textrm{ }>\textrm{ }2(x+6+11)\end{equation}