Complete Guide Linear Expressions
A linear expression is a mathematical expression that consists of constants and variables raised to the power of one. The general form is ax + b, where x is a variable, and a and b are constants. This guide will walk you through evaluating, writing, and identifying equivalent linear expressions with interactive examples.
1. Evaluate Linear Expressions
Example: Evaluate 5x + 3 for x = 4
2. Write Variable Expressions: Word Problems
Example: Concert Ticket Costs
A concert ticket website charges a $4.50 service fee per order and each ticket costs $75. Write an expression for the total cost of buying t tickets.
3. Identify Equivalent Linear Expressions
Example: Are 3(x + 4) and 3x + 12 equivalent?
Use the distributive property to simplify the first expression and see if it matches the second one.
3(x + 4)
Expression 2: 3x + 12
4. Identify Equivalent Expressions in Word Problems
Example: Phone Plan Costs
A phone plan costs $20 per month plus $5 per gigabyte of data used. Which of the following expressions represent the cost for a month where g gigabytes are used?
A) 5g + 20
B) 20g + 5
C) 20 + 5g
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