Study Guide - Unit 2: Reasoning with Equations and Inequalities (Part A)

Name ______Date ______Period ______

1. Complete the table by solving the equation and writing the property that justifies each step.

Equation / Steps
/ Original Equation

2. Solve the following equation in two different ways: 8(2x – 1) = 56

3. Ms. Wilson walked around her classroom and took snapshots of 4 different students work to display on the bulletin board for open house. Which of the following students work would best represent the Symmetric Property used correctly?

4. Mr. Jessup was explaining to the students how they can multiplyten to each side of an equation without changing the equality of the equation. Which property was he describing to the students?

5. A student rewrote 2(7x + 4) as 14x + 4. What property was the student trying to use and what was the student’s error?

6. It takes two operations to solve the following equation:

Which of the statements describes a valid approach a student might use to solve the equation?

  1. Subtract 9 from each side; multiply each side by 3
  2. Subtract 9 from each side; divide each side by 3
  3. Multiply 3 to each side; subtract 9 from each side
  4. Multiply 3 to each side; add 9 from each side

7. Al and Mandy were working together on their unit 2 math study guide. When comparing answers, they noticed that they solved #5 using two different methods, but both students arrived at the same solution. Both students insist that they solved the problem correctly. The teacher over hears their argument and asks to see their work, which is displayed below.

Mandy’s work:Al’s work:

Which conclusion did the teacher reach about their work?

  1. Only Al solved the equation using mathematical properties correctly.
  2. Only Mandy solved the equation using mathematical properties correctly.
  3. Neither Al nor Mandy solved the equation using mathematical properties correctly.
  4. Both Al and Mandy solved the equation using mathematical properties correctly.

8. Solve the equation below for the given variable.

14(3 – 7x) = –(3 + 2x)

9. Solve the equation below for the given variable; round to the nearest hundredths place.

2.39x + 4.82 = 9.37 + 6.55x

10-12 Match the equation on the left with the correct answer on the right.

10. 2x – 15 = 3(2x – 5)A. No Solution

11. 8(3x + 2) = 2(12x – 5)B. Infinitely Many Solutions

12. 3(x – 1) = 3x – 3 C. x = 0

13. Solve the following inequality: 2x + 3x ˂ 4x + 1 Graph your solution on a number line.

14. Solve the following inequality: Graph your solution on a number line.

15-16Solve for the indicated variable.

15. Simple Interest: 16. Surface area of a regular pyramid:

I = PrtS = B + ½ PL

Solve for t: Solve for L:

17-20 Create an equation or inequality to answer the questions below.

17. A small plot of land is in the shape of a rectangle. The length is 7 meters longer than the width. The perimeter of the rectangle is 86 meters. Find the width of the rectangle.

18. Janae` is shopping for a new bike. The sales tax is 6% and she has a total of $159 to spend. She finds two bikes that she loves; a green one and a pink one. The green one costs $154.99 and the pink one costs $149.99. What bike can Janae` afford to purchase?

19. Two cars travel the same distance. The first car travels at a rate of 40 miles per hour and reaches its destination in t hours. The second car travels at a rate of 55 miles per hour and reaches its destination 3 hours earlier than the first car. How long does it take for the first car to reach its destination?

20. Your school band has $812 in their account and they need to buy new percussion equipment that will cost $2, 450. If they sell sandwiches at $3.50 each, they will make exactly enough money for the equipment. If they make the same amount of sandwiches but charge $3.75 each, how much extra money will they make?