Combine the like terms to create an equivalent expression.
[tex]4 r+14-r-6=[/tex]
Answer (2)
The expression 4 r + 14 − r − 6 simplifies to 3 r + 8 by combining like terms. The variable terms 4 r and − r combine to 3 r , while the constant terms 14 and − 6 add up to 8 . Thus, the final answer is 3 r + 8 .
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Combine the 'r' terms: 4 r − r = 3 r .
Combine the constant terms: 14 − 6 = 8 .
Form the equivalent expression by adding the results: 3 r + 8 .
The equivalent expression is 3 r + 8 .
Explanation
Understanding the Expression We are asked to combine like terms in the expression 4 r + 14 − r − 6 . This involves grouping the terms with the variable r and the constant terms separately.
Combining 'r' terms First, let's identify and combine the terms containing the variable r . We have 4 r and − r . Combining these gives us: 4 r − r = ( 4 − 1 ) r = 3 r
Combining Constant Terms Next, let's identify and combine the constant terms. We have 14 and − 6 . Combining these gives us: 14 − 6 = 8
Forming the Equivalent Expression Now, we combine the results from the previous steps to form the equivalent expression: 3 r + 8
Final Answer Therefore, the equivalent expression is 3 r + 8 .
Examples
Combining like terms is a fundamental skill in algebra, used in various real-life scenarios. For example, imagine you are buying items at a store. You purchase 4 apples (represented by '4r') and later return one apple ('-r'). You also have a gift card worth $14 and spend $6. Combining like terms helps you quickly calculate the total number of apples you have (3 apples or '3r') and the remaining balance on your gift card ($8), resulting in a simplified understanding of your resources: 3 r + 8 .
