Which of the following expressions is equivalent to $5 x-4-8 x+10$?
A. $-3 x+6$
B. $-3 x-6$
C. $-3 x+14$
D. $-3 x-14$
Answer (1)
Combine the x terms: 5 x − 8 x = − 3 x .
Combine the constant terms: − 4 + 10 = 6 .
Form the equivalent expression: − 3 x + 6 .
The equivalent expression is − 3 x + 6 .
Explanation
Understanding the Problem We are asked to find an expression that is equivalent to 5 x − 4 − 8 x + 10 . This involves combining like terms, which are the terms with the variable x and the constant terms.
Combining x Terms First, let's combine the terms with x : 5 x − 8 x . This is the same as ( 5 − 8 ) x , which simplifies to − 3 x .
Combining Constant Terms Next, let's combine the constant terms: − 4 + 10 . This simplifies to 6 .
Forming the Equivalent Expression Now, we combine the simplified x term and the simplified constant term to get the equivalent expression: − 3 x + 6 .
Selecting the Correct Option Finally, we compare our simplified expression, − 3 x + 6 , with the given options. Option A is − 3 x + 6 , which matches our result.
Examples
Simplifying algebraic expressions is a fundamental skill in mathematics and has practical applications in various fields. For example, suppose you are buying items at a store. You want to buy 5 apples that cost x dollars each and you have a coupon for $4 off your total purchase. Later, you decide to buy 8 more apples at the same price but you also get an additional discount of $10. The total cost can be represented as 5 x − 4 − 8 x + 10 . Simplifying this expression to − 3 x + 6 helps you quickly calculate the final cost. If each apple costs 0.50 , t h e t o t a l cos tw o u l d b e -3(0.50) + 6 = -1.50 + 6 = $4.50.
