Select the expression that is equivalent to $3(2 x+5)-4 x$.
A. $2 x+15$
B. $2 x+15$
C. $2 x+5$
D. $x+8$
Answer (2)
Expand the expression: 3 ( 2 x + 5 ) − 4 x = 6 x + 15 − 4 x .
Combine like terms: 6 x − 4 x = 2 x , so the expression becomes 2 x + 15 .
Compare the simplified expression with the given options.
The equivalent expression is 2 x + 15 .
Explanation
Understanding the problem We are given the expression 3 ( 2 x + 5 ) − 4 x and asked to find an equivalent expression from the options: 2 x + 15 , x + 15 , 2 x + 5 , x + 8 .
Expanding the expression First, we need to expand the given expression by distributing the 3 into the parentheses: 3 ( 2 x + 5 ) − 4 x = 3 ( 2 x ) + 3 ( 5 ) − 4 x = 6 x + 15 − 4 x .
Combining like terms Next, we combine like terms. We have 6 x and − 4 x , which combine to give 2 x . So the expression becomes: 6 x + 15 − 4 x = ( 6 x − 4 x ) + 15 = 2 x + 15.
Comparing with the options Now we compare our simplified expression 2 x + 15 with the given options. We see that it matches the first option.
Final Answer Therefore, the expression equivalent to 3 ( 2 x + 5 ) − 4 x is 2 x + 15 .
Examples
In real life, simplifying algebraic expressions can help in budgeting. For example, if you earn 2 x dollars per week and get a bonus of 5 dollars, and you work for 3 weeks, but have to pay 4 x dollars in taxes, the expression 3 ( 2 x + 5 ) − 4 x represents your total earnings after taxes. Simplifying this expression to 2 x + 15 allows you to quickly calculate your earnings for any value of x .
The expression equivalent to 3 ( 2 x + 5 ) − 4 x is 2 x + 15 . This matches options A and B. Therefore, the correct choice is 2 x + 15 .
;
