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.
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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