Step-by-Step Learning
Learn about Preparation for Algebra through these example problems with detailed step-by-step solutions.
Example 1: Understanding Variables
If 'a' represents the number of apples you have, and you get 5 more apples, write an expression for the total number of apples.
Step 1: Identify what the variable 'a' represents. It represents the initial number of apples.
Step 2: Understand the action: you get 5 *more* apples. The word "more" indicates addition.
Step 3: To find the total number of apples, you need to add the initial number ('a') and the number of apples you got (5).
Step 4: Write the expression by combining the variable and the number with the addition sign.
Step 5: The expression for the total number of apples is $a + 5$.
Example 2: Writing Simple Expressions
Write an algebraic expression for "8 less than a number 'y'".
Step 1: Identify the unknown quantity, which is "a number 'y'". This is represented by the variable 'y'.
Step 2: Understand the phrase "8 less than". This means we are subtracting 8 from the number 'y'.
Step 3: The order of subtraction is important. "8 less than y" means you start with 'y' and subtract 8.
Step 4: Write the expression using the variable, the number, and the subtraction sign in the correct order.
Step 5: The algebraic expression is $y - 8$.
Example 3: Solving Simple Equations (Finding the Unknown)
Find the number that makes the equation true: $5 + \text{?} = 12$.
Step 1: Understand the equation. It says that when you add 5 to an unknown number (represented by '?'), the result is 12.
Step 2: We need to find the value of the unknown number.
Step 3: Think about what number you add to 5 to get 12. You can count up from 5 or use subtraction.
Step 4: Using subtraction, subtract 5 from 12: $12 - 5 = 7$.
Step 5: So, the unknown number is 7.
Step 6: Check your answer by substituting 7 back into the original equation: $5 + 7 = 12$. This is true.
Step 7: Therefore, the number that makes the equation true is 7.
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