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# Learn How To Evaluate Algebraic Expression

### Key Concepts

• Write expression to represent situations
• Evaluate expressions
• Write and evaluate expressions

## What is meant by algebraic expressions?

An algebraic expression (or) a variable expression is a combination of terms by the operations such as addition, subtraction, multiplication, division, etc.

Thus, we can say that 5x + 7 is an example of an algebraic expression.

Evaluate 5x + 8 when x=3.

### 4.1.1 Write expression to represent situations

Kelvin started with $217 in her bank account. He deposits$25.50 each week and never withdraws any money. What expression can Kelvin use to determine his account balance after w weeks?

Solution:

Draw a bar diagram to represent the amount of money in his account balance after w weeks.

Use the bar diagram to write an expression to represent the amount of money in the balance after w days.

Kelvin can use the expression $217 +$ 25.50w to determine the amount of money in her account balance after w weeks.

### 4.1.2 Evaluate expressions

The cost to rent a scooter is $15.50 per hour and the cost to rent a watercraft is$22.80 per hour.

Use the expression $15.5s+22.8w to determine how much it would cost to rent a scooter for 3½ hours and a watercraft for 1¾ hours. Solution: Evaluate expression for the given values.$ 15.5. s+22.8w

15.5(3 1/2 ) +22.8 (1 3/4  )

54.25 + 39.9

94.15

It cost $94.15 to rent a scooter for (3½) hours and Watercraft for (1¾) hours. ### 4.1.3 Write and evaluate expressions Example1: Ria earns$8.74 per hour plus a gas allowance of $3.50 per day at her job. How much does Ria job pay in a day when she works 5½ hours? Write an expression and evaluate for 5½ hours. Solution: Write an expression to represent how much Ria earns. Evaluate the expression for the given values. 5 ½(h)+ 3.50 = 5½ (8.74) +3.50 =11/2(8.74) +3.50 =48.07 +3.50 =51.57 Ria’s job pays$51.57 in a day.

Example2:

Mark bought a new sweater for $27 plus sales tax t. Tax was$1.76, what is the total cost of the sweater?

Solution:

Write an expression to represent the total cost of the sweater.

$27.00+ t$ 27.00 + $1.76$ 28.76

The total cost of the sweater was $28.76. ## Exercise: 1. What is the value of when x= 0.5? 2. What is the value of 7.4 n – 3.6 when n= 4 and p= 4? 3. Evaluate expression. 4d – 5 d = 1.3 4. Evaluate the expression. i. 0.4f- 3.4g ii. f= 10; g= 2 5. Evaluate 2t–5 when t=6. 6. Pizza Place bases its pizza prices on the size of the pizza and the number of toppings. The price of a medium pizza, in dollars, is 9+2t, where ‘t’ is the number of toppings. What is the price of a medium pizza with 3 toppings? 7. James is an electrician. He charges$45 per hour and spends $20 a day on gasoline. Write an algebraic expression to represent his earnings for one day. 8. A movie streaming service charges a one-time membership fee of$4 plus $13 per month. Write an expression to represent the cost of the streaming service for m months. 9. The rent cost for a bike is$15 plus \$2 for each hour the bike is used. How much will it cost if you rent the bike for a certain number of hours? Write the expression that would give you the cost.
10. Evaluate the given expression for m = 13.
m2 + m – 54

### What have we learned:

• Understand algebraic expressions.
• Write expressions to represent situations.
• Understand how to evaluate expressions.
• Write and evaluate expressions

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