Topic 1 Review
1. Tell which set or sets the number below belongs to: natural numbers, whole numbers,
integers, rational numbers, irrational numbers, or real numbers.
17
2. Write the numbers in decreasing order.
−20, −1.24, −2√5, 2.37,
8
5
3. Solve the equation. Check your answer.
23 = 5𝑥 + 2 − 2𝑥
4. Solve the equation.
5(3𝑥 + 8) = −14 + 24
5. Solve the equation for x.
2
1
𝑥− =1
9
3
6. Anna bought 8 tetras and 2 rainbow fish for her aquarium. The rainbow fish cost $6 more
than the tetras. She paid a total of $37.
7. Solve the equation. Check your solution.
6 + 8𝑞 = 11 + 7𝑞
8. Solve the equation for x.
3(𝑥 + 2) − 5 = 6𝑥 − 3(−2 + 𝑥)
9. Solve the formula for the indicated variable.
𝐷 = 𝐴𝐵𝐶 𝑠𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 𝐵
10. Solve for y.
9𝑥 − 4𝑦 = 15
11. Solve the inequality.
𝑥+9<5
12. Solve the inequality. Check your solutions.
9𝑦 + 2 ≤ 20
13. Solve the inequality and graph the solution.
−4𝑥 ≤ 16
14. The telephone company offers two billing plans for local calls. Plan 1 charges $23 per
month for unlimited calls and Plan 2 charges $16 per month plus $0.05 per call. Use an
inequality to find the number of monthly calls for which Plan 1 is more economical than
Plan 2.
15. Solve the compound inequality. Graph the two inequalities.
𝑥 ≤ −5 𝑜𝑟 𝑥 ≥ 3
16. Solve the compound inequality.
5(𝑥 − 4) < 25 𝑜𝑟 𝑥 + 7 > 13
17. Solve.
|𝑥| − 5 = 3
18. Solve the following absolute value equation.
|𝑥 − 4| = −5
19. Solve the inequality. Graph the solution set.
|𝑥| + 2 > 4
20. Two of the most expensive cars in the world are car A and car B. The prices of these two
cars differ by more than $10,000. The price of car A is $131,745.
a. Assuming that you do not know which model is more expensive, write an absolute
value inequality that describes this situation. Use x for the price of car B?
b. What are the possibilities for the price of car B?