Subtract $(4 x-1)$ from $4(5 x+7)$
A) $24 x+29$
B) $16 x+27$
C) $24 x+27$
D) $16 x+29$
Answer (1)
Distribute the 4: 4 ( 5 x + 7 ) = 20 x + 28 .
Subtract the expression: ( 20 x + 28 ) − ( 4 x − 1 ) = 20 x + 28 − 4 x + 1 .
Combine like terms: ( 20 x − 4 x ) + ( 28 + 1 ) .
Simplify: 16 x + 29 . The final answer is 16 x + 29 .
Explanation
Understanding the problem We are asked to subtract the expression ( 4 x − 1 ) from the expression 4 ( 5 x + 7 ) . This means we need to calculate 4 ( 5 x + 7 ) − ( 4 x − 1 ) .
Distributing the 4 First, we distribute the 4 in the expression 4 ( 5 x + 7 ) .
4 ( 5 x + 7 ) = 4 × 5 x + 4 × 7 = 20 x + 28
Subtracting the expressions Next, we subtract ( 4 x − 1 ) from ( 20 x + 28 ) .
( 20 x + 28 ) − ( 4 x − 1 ) = 20 x + 28 − 4 x + 1
Combining like terms Now, we combine like terms: ( 20 x − 4 x ) + ( 28 + 1 ) = 16 x + 29
Final Answer The result of the subtraction is 16 x + 29 . Comparing this with the given options, we see that it matches option D. Therefore, the correct answer is 16 x + 29 .
Examples
Imagine you're managing a budget. You have an initial income represented by 4 ( 5 x + 7 ) , and you need to subtract expenses represented by ( 4 x − 1 ) . Simplifying the expression helps you determine your remaining balance. This type of algebraic manipulation is useful in various financial and resource management scenarios, helping you understand how changes in variables (like 'x') affect your final outcome.
