Combine like terms: [tex]$5 x+7+4 x-3+5 y-8+7 y$[/tex]
Answer (1)
Combine the x terms: 5 x + 4 x = 9 x .
Combine the y terms: 5 y + 7 y = 12 y .
Combine the constant terms: 7 − 3 − 8 = − 4 .
The simplified expression is 9 x + 12 y − 4 .
Explanation
Understanding the Problem We are asked to combine like terms in the expression 5 x + 7 + 4 x − 3 + 5 y − 8 + 7 y . This means we need to group together terms that have the same variable and constants.
Combining x terms First, let's identify the terms with the variable x : 5 x and 4 x . Combining these gives us 5 x + 4 x = ( 5 + 4 ) x = 9 x .
Combining y terms Next, let's identify the terms with the variable y : 5 y and 7 y . Combining these gives us 5 y + 7 y = ( 5 + 7 ) y = 12 y .
Combining Constant Terms Finally, let's combine the constant terms: 7 − 3 − 8 = 4 − 8 = − 4 .
Final Answer Putting it all together, we have 9 x + 12 y − 4 .
Examples
Combining like terms is a fundamental skill in algebra. Imagine you're counting apples and bananas. If you have 5 apples and then get 4 more, you have 9 apples in total. Similarly, if you have 5 bananas and get 7 more, you have 12 bananas. Combining like terms is like adding up the same type of fruit to simplify your count. This skill is used in many areas, such as calculating the total cost of items, determining distances, and solving equations.
