Simplify the following expression:

$4-3(x+4)-3(x+1)$

Distribute the constants: − 3 ( x + 4 ) = − 3 x − 12 and − 3 ( x + 1 ) = − 3 x − 3 .
Substitute back into the original expression: 4 − 3 x − 12 − 3 x − 3 .
Combine constant terms: 4 − 12 − 3 = − 11 .
Combine x terms: − 3 x − 3 x = − 6 x . The simplified expression is − 6 x − 11 ​ .

Explanation

Understanding the Problem We are asked to simplify the expression 4 − 3 ( x + 4 ) − 3 ( x + 1 ) . This involves distributing the constants and combining like terms.

Distributing Constants First, distribute the -3 to both terms inside the parentheses in − 3 ( x + 4 ) and − 3 ( x + 1 ) : − 3 ( x + 4 ) = − 3 x − 12 − 3 ( x + 1 ) = − 3 x − 3

Substituting Back Now, substitute these back into the original expression: 4 − 3 ( x + 4 ) − 3 ( x + 1 ) = 4 − ( 3 x + 12 ) − ( 3 x + 3 ) = 4 − 3 x − 12 − 3 x − 3

Combining Constants Next, combine the constant terms: 4 − 12 − 3 = − 11 .

Combining x Terms Then, combine the x terms: − 3 x − 3 x = − 6 x .

Simplified Expression Finally, write the simplified expression: − 6 x − 11 .


Examples
Simplifying algebraic expressions is a fundamental skill in mathematics and has numerous real-world applications. For example, suppose you are planning a party and need to calculate the total cost. You might have a fixed cost for the venue and variable costs depending on the number of guests. By simplifying an expression that represents the total cost, you can easily determine how much you'll spend based on the number of attendees. This skill is also useful in budgeting, financial planning, and many other practical scenarios where you need to manage and optimize resources.

Answered by GinnyAnswer | 2025-07-03

To simplify the expression 4 − 3 ( x + 4 ) − 3 ( x + 1 ) , first distribute the constants and then combine like terms. This results in the simplified expression − 6 x − 11 .
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Answered by Anonymous | 2025-07-04