Simplify this expression: $4(1-3 x)+7 x-8$

Distribute the constant: 4 ( 1 − 3 x ) = 4 − 12 x .
Combine the x terms: − 12 x + 7 x = − 5 x .
Combine the constant terms: 4 − 8 = − 4 .
The simplified expression is − 5 x − 4 ​ .

Explanation

Understanding the Problem We are asked to simplify the expression 4 ( 1 − 3 x ) + 7 x − 8 . This involves distributing the 4 across the terms inside the parentheses, and then combining like terms to arrive at a simplified expression.

Distributing the Constant First, distribute the 4 to both the 1 and the − 3 x inside the parentheses: 4 ( 1 − 3 x ) = 4 × 1 − 4 × 3 x = 4 − 12 x So, the expression becomes: 4 − 12 x + 7 x − 8

Combining Like Terms Next, we combine the like terms, which are the terms with x and the constant terms. Combining the x terms: − 12 x + 7 x = ( − 12 + 7 ) x = − 5 x Combining the constant terms: 4 − 8 = − 4 So, the simplified expression is: − 5 x − 4

Final Answer Therefore, the simplified expression is − 5 x − 4 .


Examples
Simplifying algebraic expressions is a fundamental skill in algebra and is used in many real-world applications. For example, if you are calculating the total cost of items with a discount and sales tax, you might need to simplify an expression to find the final cost. Suppose you have a coupon for a certain percentage off and then have to pay sales tax. Simplifying the expression allows you to easily calculate the final cost without having to do each step separately.

Answered by GinnyAnswer | 2025-07-03

The simplified expression of 4 ( 1 − 3 x ) + 7 x − 8 is − 5 x − 4 . We achieve this by distributing the 4 , combining like terms for both the x terms and the constants. The final result is − 5 x − 4 ​ .
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Answered by Anonymous | 2025-07-04