**Adding and subtracting algebraic expressions worksheet :**

Worksheet on adding and subtracting algebraic expressions is much useful to the students who are at the initial stage of learning Algebra.

1. Simplify the expression given below.

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

2. Simplify the expression given below.

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

3. Simplify the expression given below.

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

4. Simplify the expression given below.

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

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.

**Problem 1 : **

Simplify the expression given below.

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

**Solution : **

**Step 1 : **

Group the like terms

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

**Step 2 : **

Simplify

10x - 4

Hence, (3x + 1/2) + (7x - 4 1/2) = 10x - 4

**Problem 2 : **

Simplify the expression given below.

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

**Solution : **

**Step 1 : **

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

Hence, (3x + 1/2) + (7x - 4 1/2) = -1.75x - 4.4

**Problem 3 : **

Simplify the expression given below.

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

**Solution : **

**Step 2 : **

Group the like terms

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

**Step 3 :**

Simplify

6.5x - 2.6y + 4z + 8

Hence,

(5x - 3y + 4z) + (1.5x + 0.4y + 8) = 6.5x - 2.6y + 4z + 8

**Problem 4 : **

Simplify the expression given below.

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

**Solution : **

**Step 1 : **

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

Hence, (2a - 3b + c) - (4b - 3a + c) = 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

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

After having gone through the stuff given above, we hope that the students would have understood "Adding and subtracting algebraic expressions worksheet".

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