Simplify this expression: [tex]$12 a+7 x-3 a-2 x$[/tex]
Answer (1)
The expression 12 a + 7 x − 3 a − 2 x is simplified by combining like terms. The 'a' terms are combined: 12 a − 3 a = 9 a . The 'x' terms are combined: 7 x − 2 x = 5 x . The simplified expression is 9 a + 5 x .
Explanation
Understanding the Expression We are asked to simplify the expression 12 a + 7 x − 3 a − 2 x . This involves combining 'like terms', which are terms that have the same variable raised to the same power. In this case, we have terms with the variable 'a' and terms with the variable 'x'.
Grouping Like Terms First, let's group the like terms together. We have 12 a and − 3 a as like terms, and 7 x and − 2 x as like terms. So we can rewrite the expression as ( 12 a − 3 a ) + ( 7 x − 2 x ) .
Combining Coefficients Now, we combine the coefficients of the like terms. For the 'a' terms, we have 12 − 3 = 9 , so 12 a − 3 a = 9 a . For the 'x' terms, we have 7 − 2 = 5 , so 7 x − 2 x = 5 x .
Final Simplified Expression Therefore, the simplified expression is 9 a + 5 x .
Examples
Simplifying algebraic expressions is a fundamental skill in algebra and is used in many real-world applications. For example, suppose you are buying 'a' apples at $12 each and 'x' oranges at $7 each. You have a coupon for a discount of $3 per apple and $2 per orange. The expression 12 a + 7 x − 3 a − 2 x represents the total cost after applying the discounts. Simplifying this expression to 9 a + 5 x allows you to quickly calculate the total cost for any number of apples and oranges after the discount.
