Algebra-1 Problems

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 9/4

\begin{equation}x\textrm{ }>\textrm{ }\frac{9}{4}\end{equation}

3.

Write the inequality for: 9 less than 5 times x is more than 36

\begin{equation}5x-9\textrm{ }>\textrm{ }36\end{equation}

4.

A weaver spends $ \$800 $ 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{ }800\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, 87 and 65. Write the reduced inequality for possible scores you can get on the last test and still have an average of at least 303/4.

\begin{equation}\frac{62+87+65+x}{4}\textrm{ }\ge\textrm{ }\frac{303}{4}\end{equation}

7.

You are in charge of buying the flowers for the flower beds around your school. You cannot spend over $ \$126 $ on flowers. The flowers cost $ \$18 $ for a flat of flowers. Write the reduced inequality for the possible number of flats of flowers you can buy.

\begin{equation}18x\textrm{ }\le\textrm{ }126\end{equation}

8.

Peter wants to promote his band on the Internet. Site A offers website hosting for $\$4$ per month and a startup fee of $\$79$. Site B offers website hosting for $\$103/6$ 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}4x+79\textrm{ }>\textrm{ }\frac{103}{6} \times x\end{equation}

9.

Sania needs to read to atleast $105$ pages of a book for homework. She has read $67$ pages already. Write the reduced inequality for the number of pages she needs to read to complete her homework.

\begin{equation}67+x\textrm{ }\ge\textrm{ }105\end{equation}

10.

George has a strip of wood trim that is $ 35 $ ft long. He needs $ 5 $ ft pieces to trim some windows. Write the reduced inequality for the possible number of pieces he can cut.

\begin{equation}5x\textrm{ }\le\textrm{ }35\end{equation}

11.

At an online bookstore, Sandra bought $4$ copies of the same book for the members of her book club. She got free shipping because the total price was at least $\$64$. Write the reduced inequality for the price of each book.

\begin{equation}4x\textrm{ }\ge\textrm{ }64\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: 1x, x + 3 and 17?

\begin{equation}1x+x+3\textrm{ }>\textrm{ }17\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 10.

\begin{equation}(x+9) \times 10\textrm{ }>\textrm{ }2(x+9+10)\end{equation}