Which of the following expressions is equal to the expression $4 x-2(3 x-9)$?
A. $18-2 x$
B. $-10 x-18$
C. $-2 x-18$
D. $10 x-18$

Distribute the -2: − 2 ( 3 x − 9 ) = − 6 x + 18 .
Combine like terms: 4 x − 6 x + 18 = − 2 x + 18 .
Rewrite the expression: − 2 x + 18 = 18 − 2 x .
The equivalent expression is 18 − 2 x ​ .

Explanation

Understanding the Problem We are given the expression 4 x − 2 ( 3 x − 9 ) and asked to find an equivalent expression from the options: A. 18 − 2 x B. − 10 x − 18 C. − 2 x − 18 D. 10 x − 18

Plan of Action To find the equivalent expression, we need to simplify the given expression by distributing the − 2 and combining like terms.

Distributing the -2 First, distribute the − 2 into the parentheses: − 2 ( 3 x − 9 ) = − 2 ( 3 x ) − 2 ( − 9 ) = − 6 x + 18

Combining Terms Now, combine this result with the first term 4 x :
4 x − 2 ( 3 x − 9 ) = 4 x + ( − 6 x + 18 ) = 4 x − 6 x + 18

Simplifying the Expression Simplify the expression by combining the x terms: 4 x − 6 x + 18 = ( 4 − 6 ) x + 18 = − 2 x + 18

Rewriting the Expression Rewrite the expression to match the options: − 2 x + 18 = 18 − 2 x

Choosing the Correct Option Now, compare the simplified expression 18 − 2 x with the given options: A. 18 − 2 x B. − 10 x − 18 C. − 2 x − 18 D. 10 x − 18 The simplified expression matches option A.

Final Answer Therefore, the expression 4 x − 2 ( 3 x − 9 ) is equal to 18 − 2 x .


Examples
Understanding how to simplify algebraic expressions is crucial in many real-world scenarios. For example, imagine you are calculating the total cost of items with a discount. If you have an expression like 4 x − 2 ( 3 x − 9 ) , where x represents the cost of an item, simplifying it to 18 − 2 x makes it easier to quickly compute the final cost for different values of x . This skill is also useful in budgeting, financial planning, and even in physics when dealing with equations of motion.

Answered by GinnyAnswer | 2025-07-03

The expression 4 x − 2 ( 3 x − 9 ) simplifies to 18 − 2 x , which corresponds to option A. Therefore, the correct choice is A. 18 − 2 x .
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Answered by Anonymous | 2025-07-04