Question

is this simplification correct? please explain why or why not (4 points):
4(2x + 9) + 2x - 3 simplifies to:
8x + 9 +2x -3 = 10x + 6

Explanation:

Step1: Distribute the 4

To simplify \( 4(2x + 9) + 2x - 3 \), first distribute the 4 into the parentheses. Using the distributive property \( a(b + c)=ab + ac \), we get \( 4\times2x + 4\times9+2x - 3 \), which is \( 8x + 36+2x - 3 \).

Step2: Combine like terms

Now combine the \( x \)-terms and the constant terms. The \( x \)-terms are \( 8x \) and \( 2x \), so \( 8x+2x = 10x \). The constant terms are \( 36 \) and \( - 3 \), so \( 36-3=33 \). Thus, the simplified form should be \( 10x + 33 \). In the given simplification, when distributing 4 to 9, they got 9 instead of \( 4\times9 = 36 \), so the simplification is incorrect.

Answer:

The simplification is incorrect. The correct simplification is \( 10x + 33 \) (the error was in the distribution of 4 to 9, where they used 9 instead of \( 4\times9 = 36 \)).