Simplify the following by combining like terms.
1. 2x-3y-4x+5y
2. 2.5g-6h+5g-3.4h
3. 23g+6g-7h- 47h
4. 0.25n-9+9+7n
5. -25-65r+r-15
Expand the following with distribution.
6. -2(-3x-4)
7. 15-43x+18
8. -3.5(-6r+2.4)
9. 0.4(4.6f-3.7g)
10. -8358k-34m
Expand and then simplify the following expressions.
11. - 34(n-1)+2n
12. -2.3(-3-x)-6.5x
13. -6x-8(x+7)
14. 2(3w+4)-(2w-5)
15. -122x-3y+4(-3x-y)
16. 2.6(-1.4c-4)-0.5(8c+9)
17. 2713p-4+8
18. 3.7r+2(8.6r-2.5s)
Factor the following expressions.
19. 14x-6
20. -25p+35
21. -22r-66
22. 36t-18k
23. -15k+15y
24. -4y+7
Write an expression described below. Then simplify the expression.
25. Add the expressions 3x+7 and 5x-4.
26. Subtract the expressions 22d+8 and 13d+4.
27. Add the expressions 2.8v-1.7 and -4.1v+3.8.
28. Subtract the expressions 57b-29 and -57b-49.
Read each of the problems below and follow the directions for each.
29. A gallon of gasoline costs g dollars. Paul puts 12.5 gallons of gasoline in his car and 0.75 gallon of gasoline in a portable tank. Which shows how many dollars he spent on gasoline?
a. 13.25g
b. 12.8g
c. 12.5g+0.75
d. 12.5+0.75+g
30. Lillian buys a jacket for j dollars. She must pay 7% sales tax on her purchase. Which expression represents how many dollars she will pay in all, including sales tax?
a. 1.7j
b. 1.07j
c. 7j
d. j+0.07
31. Ms. Lee sells her house for d dollars. Her real-estate agent collects a 3% commission on the sale price. Write an expression, in simplest form, to represent how many dollars Ms. Lee will receive from the sale of her house after the agent’s commission is deducted from the sale price. Show or explain your work.
32. An electrician bought 78 meter of copper wire from a hardware store at a cost of c dollars per meter. The electrician used 34 meter of the copper wire for a job. Write an expression, in simplest form, to show the dollar value of the copper wire he did not use. Show or explain your work.
33. Identify the missing addend in 3.58n+___= 0. Explain how you determined the answer.
34. A restaurant sells sandwiches for d dollars. To keep up with rising costs, the owner will increase the price of each sandwich by 10%. Write an expression to represent the new cost of a sandwich. Then simplify it.
35. Kenny earns $150 for each ring he sells. He pays $85 in rent each day for his booth at a craft festival. After the cost of renting the booth is deducted, he earns (150r-85) per day. Which expression shows how many dollars he earns in 4 days at the festival?
a. 515
b. 260r
c. 600r-85
d. 600r-340
36. Last year, the Hurst’s went to the fair as a family 3 times and paid a total of (9a+15c) dollars for tickets for all 3 of those trips. Assuming they paid the same amount each time, which expression best represents how many dollars they paid each time?
a. 27a+45c
b. 3(3a+5c)
c. 3a+5c
d. 3a+c
37. For her salary each day as a pizza delivery person, Eva earns $50 plus $2 for each pizza, p, delivered, or (50+2p) dollars. Write an expression to show the total salary Eva will earn, in dollars, if she delivers p pizzas each day for seven days. Then expand that expression. Show or explain your work.
38. Another pizza parlor offers Eva a job. The owner of that pizza parlor says that he will pay Eva a total of (120+6p) dollars if she delivers p pizzas per day for 3 days. Will the new job pay more or less than her current job (described in the question above)? Use factoring to determine and explain how you made your comparison.
39. Explain why you should perform the distributive property in the expression 4x+3(2x+1) before simplifying it any other way. Then simplify.
40. Grapes are on sale for 15% off the original price.
a. Write two expressions to show how much they are now with g being the original price.
b. If they were originally $5, how much are they now?
41. Janice lost 4% of the weight that she was last year.
a. Write two expressions to show how much she weighs now with w standing for weight.
b. If she weighed 140 pounds last year, how much does she weigh now?
42. John donates 12% of his earnings each month to a local charity. Let e be his earnings.
a. Write two expressions to show how much of his check he actually keeps.
b. Write an expression to show how much he would keep after a year of donating.
43. While exploring the sea, Ariel found a ring that will make her hair grow 4% each day. Let h be how long her hair is.
a. Write two expressions to show how long her hair would grow after one day.
b. If her hair was originally 14 inches long, how long would it be after 1 day?
44. A model house that runs completely on renewable energy uses7windmills and12solar panels. The power output of each windmill isw, and the power output of each solar panel iss.
a. Write an expression that represents the power output of 1 renewable energy house.
b. Write 2 expressions that represents the power output of 4 renewable energy houses.