### Algebra-1 Problems

Problem # |
Problem Statement |
Problems Similar To |
---|---|---|

1. |
Write the inequality for: x is less than 2 |
\begin{equation}x\textrm{ }<\textrm{ }2\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: 6 less than 10 times x is more than 64 |
\begin{equation}10x-6\textrm{ }>\textrm{ }64\end{equation} |

4. |
A weaver spends $ \$400 $ 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{ }400\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 86, 62 and 96. Write the reduced inequality for possible scores you can get on the last test and still have an average of at least 157/2. |
\begin{equation}\frac{86+62+96+x}{4}\textrm{ }\ge\textrm{ }\frac{157}{2}\end{equation} |

7. |
You are in charge of buying the flowers for the flower beds around your school. You cannot spend over $ \$45 $ on flowers. The flowers cost $ \$9 $ for a flat of flowers. Write the reduced inequality for the possible number of flats of flowers you can buy. |
\begin{equation}9x\textrm{ }\le\textrm{ }45\end{equation} |

8. |
Peter wants to promote his band on the Internet. Site A offers website hosting for $\$2$ per month and a startup fee of $\$83$. Site B offers website hosting for $\$97/7$ 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}2x+83\textrm{ }>\textrm{ }\frac{97}{7} \times x\end{equation} |

9. |
Sania needs to read to atleast $121$ pages of a book for homework. She has read $97$ pages already. Write the reduced inequality for the number of pages she needs to read to complete her homework. |
\begin{equation}97+x\textrm{ }\ge\textrm{ }121\end{equation} |

10. |
George has a strip of wood trim that is $ 12 $ 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{ }12\end{equation} |

11. |
At an online bookstore, Sandra bought $2$ copies of the same book for the members of her book club. She got free shipping because the total price was at least $\$24$. Write the reduced inequality for the price of each book. |
\begin{equation}2x\textrm{ }\ge\textrm{ }24\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: 7x, x + 7 and 63? |
\begin{equation}7x+x+7\textrm{ }>\textrm{ }63\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 11. |
\begin{equation}(x+7) \times 11\textrm{ }>\textrm{ }2(x+7+11)\end{equation} |