unit 6 – solving equations · 2014-04-03 · 6. susan is twice as old as her brother. five years...

Unit 6 – Solving Equations

Name: ___________________

1

Equations Worksheet 1

Solve the following (use algebra tiles to solve any two ):

1.) x – 2 = 14 2.) p – 5 = 12

3.) 4 = y – 7 4.) 4 = y – 7

5.) r + 6 = 9 6.) x + 5 = 11

7.) q – 5 = 15 8.) –4 = x + 7

9.) x + 7 = 20 10.) x + 2.5 = 5

2



1.) 5x = 15 2.) 2x = 18

3.) 4p = 24 4.) 9m = 81

5.) m = 12 6.) x = 7 3 4

7.) r = 12 8.) –2 = w 5 6

9.) 3x = 9.6 10.) 4n = 12.8

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1.) 4x = 12 + 8 2.) 3p 4 = 17

3.) 7m + 2m = 27 4.) 6p + 2p = 56

5.) 2s + s = 6 + 24 6.) 2x –5x = 15

7.) 9y + y = 50 8.) 16 = 2n + 6n

9.) 3 + y = 11 10.) 4r + 2r – 5 = 25

5

11.) 3c – 7c = 20 – 4 12.) 2y = 5 – 8 – 9

13.) 2 + 5t = 8 – 5 14.) 2w + 3w + 6 = 19 3

15.) 3w + 5w – 4w = 6 – 11 – 8 16.) 5y – 5 + 2y = 38 + 8

17.) 3x + 1.3 = 8.8 18.) 12 – 1.2p = 16.8

19.) 4 – 3.6y = 22 20.) 18.6 + 5k = 2.6

6



1.) 7x = 3x + 24 2.) 6p = 2p + 8

3.) 18r = 10r 16 4.) 4w = 60 + 10w

5.) 6k = 24 + 14k 6.) 2y + 3y = 8y 3

7.) 6x + x = 2x 25 8.) 3f + 2f = 8 + f

8

9.) 4z z = 4z 10 10.) 14s 6s = 48 4s

11.) 21y = 205 + 75 + 47y 12.) 8y + 17y = 15 65

13.) p = 28.6 6.6 3p 14.) 2w = 5.8 6.8 4w

15.) 6t = 10.1 + 9.9 4t 16.) 14d = 0.6 + 5.4 + 8d

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1.) 3(x + 2) = 12 2.) 4(x + 3) = 4

3.) 6(a + 4) = 36 4.) 4(2d + 2) = 16

5.) 3(x + 1) 4 = 4 2x 6.) 3(d + 3) + 10 = 49 2d

7.) 8 3p = 4(p 3) + 6 8.) 4(2x 1) = 2(x 1) + 12

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9.) 2(y + 2) = 5(y 4) 3 10.) 5(n + 6) = 7 + 2(n + 2)

11.) 4(n + 5) = 40 + 2(n + 6) 12.) 3(x – 4) + (x + 5) = 5x

13.) 5(t – 2) (t – 6) = 7t + 5 14.) 4(m – 4) – (m – 3) = m – 3

15.) 9(v +3) – 4(v+ 5) = v – 13 16.) 3(t + 2) – 5(3t – 3) = 4t +5

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1. Use algebra tiles to solve each of the following (remember, unshaded is positive and shaded is negative):

a) 2x = 5 b) 4

x = 2

2. Solve algebraically:

a) 5x = 3 b) 06

x = 1

c) 4x = 8 d) x−2 = 7

13

V

3. Use algebra tiles to solve each of the following (remember, unshaded is positive and shaded is negative):

b) 2x + 3 = 9 b) 4

x − 1 = 5


b) 5x + 2 = 7 b) 0x

10 + 3 = 1

c) 4x − 6 = 1 d) −3

x − 4 = 3

14


a) x3 = 6 b) −5

p = 2

c) 5− 3m = 1 d) −g

−2 = 3

e) f5 = 5 f) −w

16 = 2

g) l9 = 3 h) t

32 = 4

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Equations Worksheet 6 Name:___________________

1. x = 1 2. 6 = p 15 5 9 36

3. m = 4 4. b = 5 35 7 28 7

5. y = y 2 6. m = m + 1 5 3 15 7 2 14

7. 4x = 3x 2 8. y 2y = 4 y 5 4 10 4 3 6 2

9. m + 5 = m + 3 10. (x + 3) = (x – 2) 4 16 8 2 3 4

11. 3n 7 = 1 12. (3x – 2) (x + 3) = 1 5 10 2 4 12 6

13. 3y 7 = y 14. 2p – 3 + 3p 5 = 4p + 7 4 12 6 3 6 9

15. 1(y + 2) = 1( 2y + 6) 16. 3x x = 3 x 2 3 4 2 8

17. q + 3 = q + 4 18. x 4 = 3 9 3 2 8

19. 2x + 1 + x 3 = 2 20. 3d 5 d + 4 = d + 3 3 5 4 6 2

Worksheet #7 Word Problems

1. When 8 is added to 3 times a number the answer is 41. What is the number?

2. A number added to twice the same number is 51. Find the number.

3. The sum of two numbers is 117. Five times the smaller number is nine more than three times the larger number. What are the numbers?

4. Find three consecutive integers whose sum is 255.

5. One fifth of a number added to one third of the same number. If the sum is 96, find the number.

6. Susan is twice as old as her brother. Five years ago, Susan was 3 times as old as her brother. Find their ages now.

7. Brad is presently 9 years older than Mary. In 8 years, 6 times Brad’s age will equal 7 times Mary’s age. Find their ages now.

8. A man is five times as old as his daughter. The man’s son is 2 years older than his sister. In 10 years the sum of their ages will be 81. How old are they now?

9. Devon is twice as old as Melanie. In four years, their ages will total 47. How old is each person now?

10. John has $5.25 in his pocket. He has twice as many dimes as nickels and 3 more quarters than nickels. How many of each type of coins does he have?

11. There are equal number of dimes, nickels and quarters. Their total value is $4.00. How many of each kind of coin are there?

12. A parking meter contains $27.05 in quarters and dimes. If there are 146 coins, how many quarters are there?

13. After winning the lottery prize of $900, Sasha, Stephanie and Mac split the money. Sasha has half of Stephanie’s amount and Mac had 3 times Stephanie’s amount. How much did each person receive?

Worksheet #8 Introduction to Inequalities

1. State 3 values of the variable that satisfy each inequality.

a) c < 7 ___________________________

b) ___________________________

c) 5 < n ___________________________

d) ___________________________

2. Write the inequality that is graphed on each number line.

a) ____________________

b) ____________________

c) ____________________

d) ____________________

3. Write an inequality to describe each situation, then graph it.

a) The gas tank in a car contains no more than 55 L of gas. _________________

b) The minimum age you must be to watch the movie is 13. _________________

Worksheet #9 Solving Inequalities

1. Match each inequality with the graph of its solution.

a) b) c) d)

i) _____

ii) _____

iii) _____

iv) _____

2. Solve, then graph each inequality.

a)

b)

c) p ≤5p3 − 6 + 8

3. Determine which of the given numbers are solutions to the inequality (you do not need to solve these first!).

a) b)–3, 0, 1 –5, 0, 5

4. Solve each inequality and graph the solution.

a) b)

c) d)

6. Nadia gets paid $1000 per month plus 5% commission on her sales. She wants to earn at least $2200 this month. Write an inequality to represent this situation, then solve it to determine how much Nadia must sell to reach her goal.

unit 6 – solving equations · 2014-04-03 · 6. susan is twice as old as her brother. five years...

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