16

Solving Equations

HOMEWORK/PRACTICE

WORKSHEETS

Solving One-step Equations

Solving Two-step Equations

Solving Two-step Equations Word Problems

Solving Multi-step Equations

Sum of Two Number Word Problems

Perimeter of a Rectangle Word Problems

Consecutive Number Word Problems

Solving Equations w/Variables on Both Sides

Solving Bigger Multi-step Equations

Solving Equations with More Than One Fraction

Solving Proportions and Algebraic Proportions

Word Problems with Proportions

Solving Absolute Value Equations

Solving One-Step Equations Name__________________________ Date________________ Period_____ Solve each equation by using inverse operations. Write your final answer in the box on the right. 1) 6 + k = 22 2) 8 + w = -10 3) 7p = 21 4) −12v = −60 5) n + 1 = −15 6) x − 5 = 14

7) −11 = m − 6 8)

€

x5

= 7

9) v − 15 = −13 10) n + 16 = 11 11) 8x = −64 12) −14p = −56

13) −5n = 40 14) −6 =

€

m3

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15)

€

r6

= −12 16) v − 3 = −5

17) −15x = 120 18) −x = −18

19) 42 = −7n 20)

€

x3

= −13

21) 14k = −28 22) −99 = −11x

23) −1 + x = −15 24) −5 =

€

k7

25) −15 = x − 15 26) y − 4 = −10

27)

€

23x = 8 28)

€

25

a = −4

29)

€

−57

h = 20 30)

€

−34

m = -9

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Solving Two-Step Equations Name _________________________

Date ________________ Per ______

Directions: Show all steps. Write your final answer in the box on the right.

1. 4x – 6 = 22 2. –4x + 6 = -42 3. –5n + 9 = –46

4. 47 = 9x + 2 5. –11x + 4 = 26 6. 38 = 12n + 2

7. 253

m

8. 834

w

9. 362

x

10. 9173

2x 11. 142

5

3x 12. 51

7

2 x

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Two-Step Equation Name_________________________

Word Problems Practice Date ________________ Per ______

Directions: Write out an equation from each description below. Solve and write your answer in

the answer box.

1. Nine less than four times a 2. Two more than negative nine times

number is fifteen. Find the number. a number is 56. Find the number.

3. Four less than twelve times a number 4. Five more than one-third of a number

is negative one-hundred. Find the is nine. Find the number.

number.

5. Eight less than a number divided by 6. Six times a number increased by

seven is two. Find the number. three is negative twenty-one. Find

the number.

7. Eleven less than the quotient of a number 8. The product of a number and five

and five is four. Find the number. decreased by six is thirty-nine. Find

the number.

9. Eight more than twice a number is negative 10. Three less than half a number is

fourteen. Find the number. five. Find the number.

Solving Multi-step Equations Name ___________________________

Date ________________ Per _______

Solve:

1. 4n - 2n = 18 2. y + y + 2 = 18 3. 7m - 3m - 6 = 6

4. -2y + 5 + 5y = 14 5. -3p + 8 - 2p = -12 6. 5 - x - x = -1

7. 9 = -3 + n + 2n 8. -13 = 2b - b - 10 9. m + 3m - 9 = 1

10. 2(p + 8) = 22 11. 5(x - 1) = 35 12. 15 = -3(2w - 1)

13. m + 5(m - 1) = 7 14. 8y - (2y - 3) = 9 15. 16 - 2(3p + 4) = 38

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Sum of Two Number Name ______________________________

Word Problems Date ________________ Period ________

1. A second number is four 2. A larger number is twelve more

times the first. Their sum is 50. than a smaller. Their sum is

Find the numbers. 84. Find the numbers.

3. A first number is nine less than a 4. The second number is five more

second. The sum of the numbers than twice a first. Their sum

is 45. Find the numbers. is 80. Find the numbers.

5. The larger number is one less 6. A first number is four more than

than three times a smaller. seven times a second. The sum of the

Their sum is 63. Find the numbers. numbers is 92. Find the numbers.

7. A backpack costs three times as much 8. Grandma’s age is four less than six

as a notebook. Together they cost $36. times Little Patty’s age. If the sum of

Find the cost of each. their ages is 80, how old is each?

9. Joey weighs five pounds less than 10. An 30 meter cable is cut so that

twice his brother. Together they weigh one piece is two meters less than

100 pounds. What are their weights? three times the other. How long is

each piece?

Perimeter of a Name _________________________________________

Rectangle Word Problems Date _____________________ Period ____________

1. A rectangle has a length two more than 2. A rectangle has a length five less than seven times the width. If the perimeter the width. If the perimeter is 14 units, is 52 units, find the width and length. find the width and length. 3. A rectangle has a length six less than 4. A rectangle has a length six times three times the width. If the perimeter the width. If the perimeter is 42 units, is 28 units, find the width and length. find the width and length. 5. A rectangle has a width one less than 6. A rectangle has a length five more than the length. If the perimeter is 30 units, twice the width. If the perimeter is 22 find the width and length. units, find the width and length. 7. A rectangle has a length one less than 8. A rectangle has a width six less than three times the width. If the perimeter is the length. If the perimeter is 16 units, is 46 units, find the width and length. find the width and length. 9. A rectangle has a length four more than 10. Challenge: A triangle has three sides. five times the width. If the perimeter is Side a is three times side b, and side c 32 units, find the width and length. is one less than side b. If the perimeter is 59 units, find the length of all three sides. (Hint: draw a picture to help you.)

Consecutive Number Name _________________________________________

Word Problems Date _____________________ Period ____________

1. Find two consecutive integers whose 2. Find three consecutive integers whose sum is 45. Find the integers. sum is 48. Find the integers.

3. Find three consecutive integers whose 4. Find three consecutive even integers sum is -147. Find the integers. whose sum is 66. Find the integers.

5. Find three consecutive even integers 6. Find three consecutive odd integers whose sum is 72. Find the integers. whose sum is 87. Find the integers.

7. Find three consecutive odd integers 8. Find three consecutive integers whose whose sum is -39. Find the integers. sum is 312. Find the integers.

9. Find four consecutive integers whose 10. Find five consecutive even integers sum is 38. Find the integers. whose sum is 50. Find the integers.

Solving Equations with Name __________________________

Variables on Both Sides Date _______________ Per _______

Solve for x. Check your answer mentally.

1. 6x – 2 = x + 13 2. 5y – 3 = 2y + 12 3. 4k – 3 = 3k + 4

4. 5m + 3 = 3m + 9 5. 8 – x = 2x – 1 6. 2n – 5 = 8n + 7

7. 3a + 4 = a + 18 8. 6b + 14 = –7 – b 9. 5a – 14 = –5 + 8a

10. 3 + 4x = 3x + 6 11. 30 – 7m = 10m – 4 12. 8x – 3 = 7x + 2

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Variables on Both Sides Name _________________________

Word Problems Date ______________ Period ______

1. Four less than five times a number is 2. One less than three times a number

the same as five more than twice the is the same as four times the number

number. Find the number. increased by two. Find the number.

3. Three less than five times a number is 4. Two more than twice a number is the

the same as three more than eight same as eight more than the number.

times the number. Find the number. Find the number.

5. Twenty-three more than twelve 6. Two more than four times a number

times a number is the same as sixty- is the same as six more than twice the

eight more than seven times a number. number. Find the number.

Find the number.

7. Three less than eight times a number is 8. One more than three times a number is

the same as seven times the number the same as the number decreased by five.

increased by two. Find the number. Find the number.

9. Eight less than a number is the same 10. Four more than twice a number is the

as one less than twice the number. same as four less than four times the

Find the number. number. Find the number.

CV

Solving Multi-step Equations Name ________________________

With Distributive Property, Combining Date ________________ Per _____

Like Terms, and Variables on Both Sides

1. 9(x + 3) = 4x – 3 2. 2(12 – 8x) = x – 11x

3. 3x + 8(2x – 6) = 2 + 14x 4. 2v + 18 = 16 – 4(v + 7)

5. 4x – (9 – 3x) = 8x – 1 6. -7(1 – 4m) = 13(2m – 3)

7. 4x + 5(7x – 3) = 9(x – 5) 8. 2(6x + 3) = 18 – 3(16 -3x)

9. 8(4u – 1) – 12u = 11(2u – 6) 10. -5 – (15y – 1) = 2(7y – 16) – y

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Solving Equations with Name _________________________

More Than One Fraction Date ______________ Per ________

Solve the following equations using the fraction busters method.

1.

x

6

2x

3 5 2.

x

3x

21 3.

x

2x

5 9

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x

3x

5

2

3 5.

x

2 4

x

3 6.

x

8x

12

1

3

7.

57x

6

3

2 8.

2x

3

3x

5 2 9.

1

5x

2

7

10

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x 3

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4x 4

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Solving Proportions Name ______________________________________ Date ______________________ Per ___________ Directions: Solve each proportion by cross multiplying. Show your steps.

1)

10

k8

4 2)

m

127

3 3)

2

x7

9 4)

x

1210

2

5)

4

92

x 6)

p

813

2 7)

10

122

n 8)

10

m4

6

9)

x

4x 2

8 10)

7

10x 3

5 11)

4

x6

x 2

12)

9

56

x 1 13)

x 4

2x 3

3 14)

2x 1

54x 2

9

15)

5

x 2

3

x 2 16)

4

2x 5

3

x 5 17)

x 6

3 5

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Word Problems with Name ______________________________________

Proportions Date _____________________ Period __________

1. An object that weighs 12 pounds on Earth, 2. A speedboat factory can produce 12 would weigh only 2 pounds on the moon. boats in 8 days. How many days will How much would a kid who weighs 84 it take the factory to produce 30 pounds on Earth, weigh on the moon? speedboats? 3. A biscuit recipe for 60 biscuits calls 4. Darwin can read 7 pages of his book in for 4 cups of flour. How much flour 5 minutes. At this rate, how long will it

is needed to make 90 biscuits? take him to read the entire 175 page book.

5. While exercising, Julie found that her heart 6. There are 1,200 calories in 8 ounces of was beating 12 times every 5 seconds. frosting, how many calories are in How many times was it beating per 5 ounces of frosting? 60 seconds?

7. If a bunny can hop 12 feet in 8 seconds, 8. At a rock concert, the ratio of men how many seconds will it take the bunny to women is 6 to 2. If there are 1,500 men, to hop 180 feet. how many women are there?

9. Party Fizz Punch is made by mixing 10. The money used in Jordan is called the 4 parts fruit juice to 3 parts Sprite. Dinar. The exchange rate is $3 to 2 Dinars.

Bill has 44 ounces of fruit juice. How Find how many Dinar you would receive if much Sprite should he mix with it? you exchanged 36 dollars.

Solving Absolute Value Name _____________________________

Equations Date _________________ Per ________

Solve (graph # 1- 6) and give the final answers that would make the equations true.

1. 3x 2. 7x 3. 42 x

4. 312 x 5. 963 x 6. 927 x

7. 62 x 8. 25 x 9. 30105 x

10. 2426 x 11. 2835 x 12. 171926 x