2.1 – 2.4 Review Worksheets
1. Find the solution set of a number, x, whose distance from 12 is greater than 31 units.
2. A scientist has two homogeneous solutions, an 80% solution of hydrochloric acid and a 30%
solution of phosphoric acid. If he has 75 milliliters of hydrochloric acid, how much phosphoric acid
must be added to create a 50% acid solution?
3. Jimmy goes to the grocery store to buy pineapples and cantaloupes. One pineapple contains 30
micrograms of vitamin A and 50 micrograms of vitamin C. One cantaloupe contains 22 micrograms of
vitamin C and 52 micrograms of vitamin A. How many pineapples and cantaloupes must Jimmy buy
to have 1,550 micrograms of vitamin A and 1,260 micrograms of vitamin A?
4. Solve for x.
4𝑥
5
+
7−𝑥
4
=6+
𝑥−2
10
5. A plane can fly from New York to Dubai (about 6,836 miles) in 15 hours, with a 30 mph tailwind. It
takes the same plane 8 hours to make the return flight to London without the tailwind (about 3,404).
What is the approximate speed at which the plane travels to and from Dubai? (assuming the average
plane speed is the same on each flight--round up to the nearest whole number)
6. Solve and write the solution in inequality and interval notation |9𝑥 − 12| ≥ 24
7. Solve for x. |𝑥 + 218|=834
8. Apple is planning on creating and selling a new iPhone. The fixed costs for production are
$32,000, and the variable costs are $49.50 per phone. The wholesale price is $57.50 per phone. How
many phones must Apple sell to break even; that is, so that costs will equal revenues?
9. Solve for x.
5𝑥 – 2
7
1
10𝑥 + 3
4
4
+ <
+1
10. Solve for x and write in interval notation. 38 + 3𝑥 ≤ −2 − 7𝑥 𝑎𝑛𝑑 − 2 − 7𝑥 < 40
11. (Disclaimer: not actual distance) A captain sailed down the Danube River (with the current) at 9
knots (nautical mph) to Budapest from Vienna in 48 hours. He returned by the same route in 72
hours. What is the speed of the current and the boat assuming the boat’s average speed is the
same?
12. Cashews are sold for $5.50/lb and M&M’s are sold for $3/lb. If a 9.75 pound mixture is sold for
$39.25, how many pounds of Cashews and M&M’s were in the mix?
13. Two pumps working together complete a job in 2 hours. If one pump working alone can complete
the same job 3 hours faster than the other, how fast can each pump complete the job alone?
14. If a factory manufactures books for $5 and sells them for $7 and has operating costs of $3000
per month, how many books does the plant need to sell in a month to make a profit?
15. Solve for x.
16. Solve for b.
17. Solve for x.
12
𝑥2
+ 5𝑥 − 24
𝑏
𝑏+ 4
=
2𝑥 − 4
6
−
−4
𝑏+ 4
21
𝑥 −3
=
11
𝑥+ 8
−3
+6 ≥ 2+
4𝑥
18. Solve for x. −4 ≤ 4 − 8𝑥 < 20
19. Solve for x. 42 = |x – 3| + 37
20. Solve for x. 8|x – 6| + 5 > – 3
8