Simplify: $5-8(1+2 x)$
A. $10 x+12$
B. $9 x+6$
C. $-3-16 x$
D. $46 x+15$
Answer (2)
Distribute the -8: 5 − 8 ( 1 + 2 x ) = 5 − 8 − 16 x .
Combine the constants: 5 − 8 = − 3 .
Write the simplified expression: − 3 − 16 x .
The simplified expression is − 3 − 16 x .
Explanation
Understanding the Problem We are given the expression 5 − 8 ( 1 + 2 x ) and asked to simplify it. This involves distributing the − 8 across the terms inside the parentheses and then combining like terms.
Distributing the -8 First, we distribute the − 8 to both the 1 and the 2 x inside the parentheses: − 8 ( 1 + 2 x ) = − 8 ( 1 ) + ( − 8 ) ( 2 x ) = − 8 − 16 x
Substituting Back Now, we substitute this back into the original expression: 5 − 8 ( 1 + 2 x ) = 5 − 8 − 16 x
Combining Constants Next, we combine the constant terms 5 and − 8 : 5 − 8 = − 3
Simplified Expression Finally, we write the simplified expression: − 3 − 16 x So, the simplified expression is − 3 − 16 x .
Examples
Simplifying algebraic expressions is a fundamental skill in mathematics with numerous real-world applications. For example, suppose a store offers a discount where you get $8 off the total price, plus an additional 2 o fff ore v ery i t e m yo u b u y . I f yo u b u y x$ items, the total discount can be expressed as 8 + 2 x . If the original price was $5, the final price can be expressed and simplified as 5 − ( 8 + 2 x ) = 5 − 8 − 2 x = − 3 − 2 x . This shows how simplifying expressions helps in understanding discounts and pricing strategies.
To simplify the expression 5 − 8 ( 1 + 2 x ) , distribute -8 to get − 8 − 16 x and then combine the constants to find − 3 − 16 x . The correct answer is option C: − 3 − 16 x .
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