Lesson 2-C Practice (2.4, 5.3) – Alg. I Honors
Solving Equations / Inequalities with Variables on Both Sides

Directions: For each word problem, write an equation/inequality, and solve (showing all required steps).

1. The product of 3 and a number is more than twice that
same number increased by 5. / 2. An apple has 25 fewer calories than a pear. If six
apples have the same calories as 4 pears, how many
calories are in both kinds of fruit?
3. Tom and Harry are watching Netflix and eating M&M’s.
Tom starts with 40 M&M’s and is steadily eating them
at a rate of 6 per minute. Harry began with 60 M&M’s
and is scarfing them down at a rate of 10 per minute.
How many minutes before Tom and Harry both have
the same amount left to eat? / 4. Georgia is choosing between two cell phone plans that
offer the same amount of free minutes. Cingular’s plan
charges $39.99 per month with additional minutes
costing $0.45 each. Verizon’s plan costs $44.99 with
any additional minutes costing $0.40 each. How many
minutes will she have to talk for both plans to cost the
same?
5. You need to mail a package. UPS charges $7 for the
first pound and $0.20 per each pound over. FedEx
charges $5 for the first pound and $0.30 for each
additional pound. How many pounds will result in
both companies charging the same amount.
When would you use UPS? FedEx? / 6. Apartment hunting! You have searched and searched
and have decided on two final choices. Hickory Winds
has a $1000 security deposit and costs $1200 each
month. Pine Woods has a $1500 deposit and a rent of
$1175. What information do you need to make a
decision?
Is there any solution that would make no difference
on the decision? If there is, what is it?
7. A full 355 mL can of Coke is leaking at a rate of 5 mL per minute into an empty can. How long will it take for the two
cans to have the same amount of Coke?

Solve each equation / inequality. (Do Not Graph.)

8. 9.

10. 11.

H.O.T Problems – (Higher Order Thinking)

12. Explain how you could solve without multiplying or dividing each side by a negative
number.

13. Create an equation with at least two grouping symbols for which there is no solution.

14. Find the value of for which each equation is an identity.  What does that mean??

a. b.

15. If has infinitely many solutions, what will be the solution of ?
Explain how you know.