# Simplifying and Combining Algebraic Terms

Please see the attached file for the fully formatted problems.

1. Simplify - 5 (7 - 2 ) - 3(4 - 7 )

- 13 - (-5 )

or in linear form [ - 5 (7 - 2 ) - 3(4 - 7 ) ] / [ - 13 - (-5 ) ]

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2. Simplify 7 - 2(14x - 2y) + 4( x -4y)

combine like terms

-28x + 4x = -24x

4y + -16y = -12y

Add it all up

7 - 24x - 12y

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3. Simplify -12  -9

35 14

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4. Evaluate the expression: 4x2 - 2x ; for x = - 3

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5. Solve for x: 4 - 2x = - 1 + x

3 6

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6. Solve for y: 5(y + 3) = -2 (y - 4)

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7. Solve the inequality for x: 2x + 8 (see attached file) - 16 + 8x

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8. Solve for x: 1 ( 4x - 6) = -3x + 2 or in linear form ( 4x - 6)/2 = -3x + 2

2

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9. Solve the inequality for x: 3(x-6) - 4 (4 - x) < x - 4

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10. Cassi's bank account exceeds Bill's by $124. The two bank accounts combined have $306. How much is in each account?

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11. After a 30% discount you pay $1155 for a tv. What was the original price of the TV?

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12. Solve t = 2s - v for s

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13. Solve the proportion for x x = x + 6 or in linear form x/8 = (x+6)/20

8 20

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14. Determine whether the order pair (-3,5) is a solution of the system

9x + 7y = 8

8x - 9y = - 69

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15. Using the addition method solve the given system of equations for x and y.

x/3 - y/2 = -5/6

and

x/5 - y/3 = -3/5

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16. Solve the given system by graphing. Use the Excel template to show how you obtained your answer and write the x and y value for the answer as an ordered pair. (The graph must be included as part of your answer.)

x - y = 4

x + y = 2

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17. Using the substitution method solve the system of equations:

y = 2x - 6

y = x - 5

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18. Find the volume of a cylinder with a diameter of 12 feet and a height of 15 feet. Round the answer to the nearest whole number.

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19 City A is 60 miles East of City B. A car leaves city a traveling East at 30 mph and at the same time a car leaves city B traveling East at 60 mph. How long will it take the car leaving from city B to catch the car leaving from city A.

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20. Complete the table of values for y = 1 x + 1 or in linear form y = x/4 + 1

4

x | 0 | 2 | 4 .

y = x/4 + 1 | | |

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21 Calculate the slope of the line passing through the given ordered pairs.

(7, -1) and (3, -2)

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22. For the equation 8x - 3y = 6 find the slope and the y intercept.

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23 Given the lines -2x + 3y = 6 and 2y + 3x = 4. What is the relationship between these lines? (Be sure to show your work and state your reason for your answer. There is no credit give for just a letter as the answer.)

a) Parallel

b) Intersecting at other than a 90 degree angle

c) Intersecting and perpendicular

d) No relationship

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24 The combined population of Town 1 and Town 2 was 25,000 in 1990. By 1995 the population of Town 1 had increased by 10% while the population of Town 2 had grown by 9%. If the total population of both towns had increased by 2380 people, what was the population of each town in 1990.

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25. Write the equation for the line passing through (2,0) and (5,3) in slope-intercept form.

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26. There are 385 surfers in the City. Two thirds of the boys are surfers and one twelfth of the girls are surfers. If there are two girls for every boy, then how many boys and how many girls are there in the city.

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27. The sum of two numbers is -16. The difference of the same numbers is 8. Find the numbers.

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28. A charity sells tickets for a fund raising dinner. Each adult's ticket costs $10 and each child's ticket costs $5. A total of $1050 was raised by selling 130 tickets. How many adult and child tickets were sold.

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29. Find the equation of the line that passes through point (4,7) and that is perpendicular to the line whose equation is y = -2x + 1.

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30. The weight of a boat varies directly with the length of the boat. If a 12 foot boat weighs 86 lbs. then what is the weight of a 14 foot boat? (Find the weight to the nearest tenth of a pound).

#### Solution Preview

Please see the attached file for the complete solution.

Solve and show the work...

1. Simplify - 5 (7 - 2 ) - 3(4 - 7 )

- 13 - (-5 )

or in linear form [ - 5 (7 - 2 ) - 3(4 - 7 ) ] / [ - 13 - (-5 ) ]

Solution:

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2. Simplify 7 - 2(14x - 2y) + 4( x -4y)

combine like terms

-28x + 4x = -24x

4y + -16y = -12y

Add it all up

7 - 24x - 12y

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3 Simplify -12 ÷ -9

35 14

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4. Evaluate the expression: 4x2 - 2x ; for x = - 3

Substitute x = -3

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5 Solve for x: 4 - 2x = - 1 + x

3 6

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6 Solve for y: 5(y + 3) = -2 (y - 4)

5y + 15 = -2y + 8

5y + 2y = 8 - 15

7y = -7

=> y = -1

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7. Solve the inequality for x: 2x + 8 ≤ - 16 + 8x

Divide each side by -6

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8. Solve for x: 1 ( 4x - 6) = -3x + 2 or in linear form ( 4x - 6)/2 = -3x + 2

2

Solution:

( 4x - 6)/2 = -3x + 2

2x - 3 = -3x + 2

2x + 3x = 2 + 3

5x = 5

⇨ x = 5/5 = 1

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9. Solve the inequality for x: 3(x-6) - 4 (4 - x) < x - 4

3x - 18 -16 + 4x < x - 4

7x - 34 < x - 4

7x - x < -4 + 34

6x < 30

Divide each side by 6

x < 5

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10. Cassi's bank account exceeds Bill's by $124. The two bank accounts combined have $306. How much is in each account?

Let Bill's account balance = x

Cassi's account = x +124

The two bank accounts combined have $306.

(x +124) + x = 306

2x + 124 = 306

2x = 182

x = 182 / 2

x = 91

Bill's account = $91

Cassi's account = $91 + 124 = $215

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11 After a 30% discount you pay $1155 for a tv. What was the original price of the TV?

Let the original price of TV be x dollars

Then

x - 30% of x = 1155

x - 0.3x = 1155

0.7x = 1155

x = 1155/0.7 = ...

#### Solution Summary

The solution assists in simplifying and combining algebraic term.