SOLVING ALGEBRAIC EXPRESSIONS WORKSHEET

Question 1 :

Given : ⁽ˣ ⁺ ʸ⁾⁄₂ = 3, find the value of (x + y).

Question 2 :

Given 5x - 3 = -4, what is the value of (10x - 6)?

Question 3 :

Given 3x + 1 = 5, find the value of (6x - 7)?

Question 4 :

Given : 7x - 1 = 7 - 3x, what is the value of (5x - 3)?

Question 5 :

-3(5 - 2x) + 8

Which of the following expressions is equivalent to the above expression?

(A) 4x - 6

(B) 4x - 7

(C) 4x + 6

(D) 4x + 7

Question 6 :

If x = -5, what is the value of the following expression?

8 - 2(4 - 5x)

Question 7 :

If p = 2 and q = -3, what is the value of the following expression?  

p² + 2q²

Question 8 :

Given : 5p + 6 = 3(q + 2), what is the value of ᵖ⁄q?

Question 9 :

Given : ³ˣ⁄y = ⅔, find the value of ʸ⁄ₓ.

Question 10 :

Given : ⁽³ˣ ⁺ ²⁾⁄y = 7, What is the value of (6x - 14y)?

Question 11 :

When 3 is subtracted from 15 times the number n, the result is 27. What number results when 7 is subtracted from 5 times n?

Question 12 :

Adding 3 to 12 times of the number y results -9. If 3 is subtracted from 4 times k, find the result.

Question 13 :

What is the value of x in the equation 

(x - 2)/3 + 1/6 = 5/6 ?

Question 14 :

Mr. Cortez drove at a constant rate for 5 hours. At the end of 2 hours he had driven 90 miles. After 5 hours, he had driven 225 miles.

a. What is the dependent variable in this relationship? __________________________

b. What is the independent variable in this relationship? __________________________

c. Can this relationship be modeled by a linear function?

Provide evidence to support your claim.

Answers

1. Answer :

⁽ˣ ⁺ ʸ⁾⁄₂ = 3

Multiply both sides by 2.

2[⁽ˣ ⁺ ʸ⁾⁄₂] = 2(3)

x + y = 6

2. Answer :

5x - 3 = -4

Multiply both sides by 2.

2(5x - 3) = -4

Distribute the 2 to both terms in the parenthses.

2(5x) + 2(-3) = 2(-4)

10x - 6 = -8

3. Answer :

3x + 1 = 5

Subtract 1 from both sides.

3x = 4

Multiply both sides by 2.

6x = 8

Subtract 7 from both sides.

6x - 7 = 1

4. Answer :

7x - 1 = 7 - 3x

Add 3x to both sides.

10x - 1 = 7

Add 1 to both sides.

10x = 8

Divide both sides by 2.

5x = 4

Subtract 3 from both sides.

5x - 3 = 1

5. Answer :

-3(5 - 2x) + 8

Distribute the -3 to both terms in the parenthses, then combine the numerical constants.

= -3(5) - 2(-2x) + 8

= -15 + 4x + 8

= 4x - 7

The correct Answer choice is (B).

6. Answer :

= 8 - 2(4 - 5x)

Substitute x = -5.

= 8 - 2[4 - 5(-5)]

= 8 - 2[4 + 25]

= 8 - 2(29)

= 8 - 58

= -50

7. Answer :

= p² + 2q²

Substitute p = 2 and q = -3.

= p² + 2q²

= 2² - 2(-3)²

= 4 + 2(9)

= 4 + 18

= 22

8. Answer :

5p + 6 = 3(q + 2)

Distribute the 3 to both terms in the parenthses.

5p + 6 = 3(q) + 3(2)

5p + 6 = 3q + 6

Subtract 6 from both sides.

5p = 3q

Divide both sides by y.

⁵ᵖ⁄q = 3

Multiply both sides by .

(⁵ᵖ⁄q)(⅕) = 3(⅕)

ᵖ⁄q = ⅗

9. Answer :

³ˣ⁄y = ⅔

Multiply both sides by ⅓.

(⅓)(³ˣ⁄y) = (⅓)(⅔)

ˣ⁄y = ²⁄₉

Take reciprocal on both sides.

ʸ⁄ₓ = ⁹⁄₂

10. Answer :

⁽³ˣ ⁺ ²⁾⁄y = 7

Multiply both sides by y.

3x + 2 = 7y

Subtract 7y from both sides.

3x + 2 - 7y = 0

Subtract 2 from both sides.

3x - 7y = -2

Multiply both sides by 2.

2(3x - 7y) = 2(-2)

Distribute the 2 to both terms in the parenthses.

2(3x) + 2(-7y) = -4

6x - 14y = -4

11. Answer :

From the given information,

15n - 3 = 27

Add 3 to both sides.

15n = 30

Divide both sides by 3.

5n = 10

Subtract 7 from both sides.

5n - 7 = 3

Subtracting 7 from 5 times n results 3.

12. Answer :

From the given information,

12y + 3 = -9

Subtract 3 from both sides.

12y = -12

Divide both sides by 3.

4y = -4

Subtract 3 from both sides.

4y - 3 = -7

Subtracting 3 from 4 times y results -7.

13. Answer :

(x - 2)/3 + 1/6 = 5/6

Least common multiple of 3 and 6 is 6.

[2(x - 2) + 1]/6 = 5/6

2x - 4 + 1 = 5

2x - 3 = 5

2x = 5 + 3

2x = 8

x = 8/2

x = 4

So, the value of x is 4.

15. Answer :

a) Number of miles crossed is dependent variable

b) Number of hours is independent variable

c) y = mx + b

(2, 90) and (5, 225)

Rate of change = (225 - 90) / (5 - 2)

= 135/3

= 45

y = 45x + b

Applying the point (2, 90), we get

90 = 45(2) + b

b = 0

y = 45x

The relationship between the quantities is y = 45x

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