Multi-Step Equations UNIT TEST, Unit 8 Lesson 10

Question

ANSWERS:

1. Add 4 to both sides

2. Multiplying both sides by 7 undoes the division of x by 7 in the original problem.

3. 12 = - x + 8

4. Divide both sides by 12

5. 35.2

6. - 1/5

7. 12.452

8. - 4.75

9. 12 (t + 10) = 180

10. $1.15

11. $1.30

12. 1.) 4 2.) 4 3.) 20 4.) 3 5.) 17

13. $0.70

14. 80,000

15. THIS QUESTION MUST BE ANSWERED IN YOUR OWN WORDS:
" Dea needs to figure out how much cheaper the ones she bought that were on sale were. She paid $1.50 less than the regular price and paid a total of $51.00 for all 6 of the tickets. To find out the regular price use: 6(p - $1.50) = $51.00.
Now simplify: 6p - 9 = 51
Add 9 to both sides: 6p - 9 + 9 = 51 + 9
6p = 60
Now divide both sides by 6: 6p/6 = 6/6 which means p = 10
This means the regular price of each ticket was $10.00
So,she bought 6 tickets that cost $51.00 total, and payed $1.50 less than the original price of $10.00 per ticket. Dea bought 6 tickets for $8.50 each which was a total of $51.00 dollars spent.

Answer 1

Here are the answers summarized and structured based on your initial response:

1. To isolate \(x\), add 4 to both sides of the equation.

2. Multiplying both sides by 7 undoes the division of \(x\) by 7 in the original problem.

3. The equation can be rewritten as: \(12 = -x + 8\).

4. To solve for \(x\), divide both sides by 12.

5. The value of \(x\) is \(35.2\).

6. The value of \(x\) is \(-\frac{1}{5}\).

7. The value of \(x\) is \(12.452\).

8. The value of \(x\) is \(-4.75\).

9. The equation is \(12(t + 10) = 180\).

10. The cost per item is $1.15.

11. The cost per item is $1.30.

12. The answers to the multi-step problems are:

1. 4
2. 4
3. 20
4. 3
5. 17

13. The cost is $0.70.

14. The total is 80,000.

15. Answer in your own words: "Dea needs to determine the original price of the tickets she purchased. She bought 6 tickets, each costing $1.50 less than the regular price, totaling $51.00. The equation to find the regular price \(p\) is 6(p - $1.50) = $51.00. Simplifying, we have: 6p - 9 = 51. Adding 9 to both sides gives us 6p = 60. Dividing by 6, we find p = $10.00. Thus, the regular price per ticket was $10.00. Since Dea paid $1.50 less, she purchased 6 tickets at $8.50 each, totaling $51.00."

This format clarifies the answers while maintaining the original math and reasoning.