2.12 One-Variable Linear Equations and Inequalities; Unit Exam - Algebra

Two trains leave the station at the same time but are headed in opposite directions. One train travels at 70 mph. The other travels at 80 mph. How much time passes until the two trains are 600 mi apart?

4 hours.

Juanita is 13 years older than her cousin. The sum of their ages is no less than 103 years. What's the youngest age Juanita's cousin can be?

45 years old.

Justify each step of the solution. Line One: 4 (4x + 6) - 7 = 77 - 4x Line Two: 16x + 24 - 7 = 77 - 4x Line Three: 16x + 17 = 77 - 4x Line Four: 20x + 17 = 77 Line Five: 20x = 60 Line Six: x = 3

Justification for each step of the solution. Line One: Given Line Two: Distributive Property (DP) Line Three: Combine Like-Terms (CLT) Line Four: Addition Property of Order (APO) Line Five: Subtraction Property of Order (SPO) Line Six: Division Property of Order (DPO)

Justify each step of the solution. Line One: -7 (3 + 8x) + 5x ≤ 1 - 62x Line Two: -21 - 56x + 5x ≤ 1 - 62x Line Three: -21 - 51x ≤ 1 - 62x Line Four: -21 + 11x ≤ 1 Line Five: 11x ≤ 22 Line Six: x ≤ 2

Justification of each step of the solution. Line One: Given Line Two: Distributive Property (DP) Line Three: Combine Like-Terms (CLT) Line Four: Addition Property of Equality (APE) Line Five: Addition Property of Equality (APE) Line Six: Division Property of Equality (DPE)

Solve for c: a = 11 + 4b - 4c

c = a - 11 - 4b/-4

Victoria is 4 years older than her neighbor. The sum of their ages is 14 years. Make an inequality that can be used to represent this situation, where x = Victoria's neighbor's age.

x + x + 4 ≤ 14

Solve for x: 4.6x < -15.64

x < -3.4

x + 15.09 = -2.57

x = -17.66

3/8 (2x + 16) - 2 = 13

x = 12

8/9x = 32

x = 36

Solve for x: -6 > -30 - 4x

x > -6

Solve for x: x - 7.67 ≥ 8.4

x ≥ 16.07