ADDING AND SUBTRACTING ALGEBRAIC EXPRESSIONS WORKSHEET  

Problem 1 : 

Simplify the expression given below. 

(3x + 1/2) + (7x - 4 1/2)

Problem 2 : 

Simplify the expression given below. 

(-0.25x - 3) - (1.5x + 1.4)

Problem 3 : 

Simplify the expression given below. 

(5x - 3y + 4z) + (1.5x + 0.4y + 8)

Problem 4 : 

Simplify the expression given below. 

(2a - 3b + c) - (4b - 3a + c)

Problem 5 : 

Jill and Kyle get paid per project. Jill is paid a project fee of $25 plus $10 per hour. Kyle is paid a project fee of $18 plus $14 per hour. Write an expression to represent how much a company will pay to hire both to work the same number of hours on a project.

Detailed Answer Key

Problem 1 : 

Simplify the expression given below. 

(3x + 1/2) + (7x - 4 1/2)

Solution : 

Step 1 : 

=  (3x + 1/2) + (7x - 4 1/2)

Group the like terms 

=  (3x + 7x) + (1/2 - 4 1/2)

Step 2 :

Simplify

=  10x - 4

Problem 2 : 

Simplify the expression given below. 

(-0.25x - 3) - (1.5x + 1.4)

Solution : 

Step 1 : 

=  (-0.25x - 3) - (1.5x + 1.4)

Distribute the negative sign to the terms in the second parenthesis.

=  -0.25x - 3 - 1.5x - 1.4

Step 2 : 

Group the like terms 

=  (-0.25x -1.5x) + (-3 - 1.4)

Step 3 :

Simplify

=  -1.75x - 4.4

Problem 3 : 

Simplify the expression given below. 

(5x - 3y + 4z) + (1.5x + 0.4y + 8)

Solution : 

Step 2 : 

=  (5x - 3y + 4z) + (1.5x + 0.4y + 8)

Group the like terms 

=  (5x + 1.5x) + (-3y + 0.4y) + 4z + 8

Step 3 :

Simplify

=  6.5x - 2.6y + 4z + 8

Problem 4 : 

Simplify the expression given below. 

(2a - 3b + c) - (4b - 3a + c)

Solution : 

Step 1 : 

=  (2a - 3b + c) - (4b - 3a + c)

Distribute the negative sign to the terms in the second parenthesis.

=  2a - 3b + c - 4b + 3a - c

Step 2 : 

Group the like terms 

=  (2a + 3a) + (-3b - 4b) + (c - c) 

Step 3 :

Simplify

=  5a - 7b

Problem 5 : 

Jill and Kyle get paid per project. Jill is paid a project fee of $25 plus $10 per hour. Kyle is paid a project fee of $18 plus $14 per hour. Write an expression to represent how much a company will pay to hire both to work the same number of hours on a project.

Solution : 

Step 1 : 

Write expressions for how much the company will pay each person. Let h represent the number of hours they will work on the project.

Jill : $25 + $10h     Kyle: $18 + $14h

  Fee + Hourly rate × Hours      Fee + Hourly rate × Hours

Step 2 : 

Add the expressions to represent the amount the company will pay to hire both.

Combine their pay : 

=  25 + 10h + 18 + 14h

Use the Commutative Property :

=  25 + 18 + 10h + 14h

Combine like terms :

=  43 + 24h

So, the company will pay 43 + 24h dollars to hire both Jill and Kyle.

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