Simplify this expression: [tex]12 a+7 x-3 a-2 x[/tex]
Answer (1)
Group like terms: Identify and group terms with the same variable.
Combine 'a' terms: 12 a − 3 a = 9 a .
Combine 'x' terms: 7 x − 2 x = 5 x .
Write the simplified expression: 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 'a' terms and 'x' terms.
Combining 'a' Terms First, let's group the 'a' terms together: 12 a − 3 a . Subtracting 3 a from 12 a gives us 9 a .
Combining 'x' Terms Next, let's group the 'x' terms together: 7 x − 2 x . Subtracting 2 x from 7 x gives us 5 x .
Final Simplified Expression Now, we combine the simplified 'a' and 'x' terms to get the final simplified expression: 9 a + 5 x .
Examples
In real life, simplifying expressions is useful in various scenarios. For example, suppose you are buying 'a' apples at $12 each and 'x' oranges at $7 each. You have a coupon for $3 off the total cost of apples and $2 off the total cost of oranges. The expression 12 a + 7 x − 3 a − 2 x represents the total cost after applying the coupons. Simplifying it to 9 a + 5 x makes it easier to calculate the final cost for any number of apples and oranges. This kind of simplification is also used in budgeting, inventory management, and other everyday calculations.
