Questions: Simplify the expression by combining like terms. -5.1 d+4.8-(2 d+0.5)+2.5 d What does -5.1 d+4.8-(2 d+0.5)+2.5 d equal? A. -7.6 d+7.3 B. -4.6 d+5.3 C. -0.3 d D. -4.6 d+4.3

Transcript text: Simplify the expression by combining like terms. \[ -5.1 d+4.8-(2 d+0.5)+2.5 d \] What does $-5.1 \mathrm{~d}+4.8-(2 \mathrm{~d}+0.5)+2.5 \mathrm{~d}$ equal? A. $-7.6 \mathrm{~d}+7.3$ B. $-4.6 \mathrm{~d}+5.3$ C. -0.3 d D. $-4.6 \mathrm{~d}+4.3$

Solution

Solution Steps

To simplify the expression, we need to combine like terms. This involves grouping the terms with the variable $d$ together and the constant terms together. We then perform the arithmetic operations to simplify the expression.

Step 1: Write the Original Expression

We start with the expression: \[ -5.1 d + 4.8 - (2 d + 0.5) + 2.5 d \]

Step 2: Distribute and Combine Like Terms

Distributing the negative sign gives us: \[ -5.1 d + 4.8 - 2 d - 0.5 + 2.5 d \] Now, we combine the $d$ terms: \[ (-5.1 d - 2 d + 2.5 d) + (4.8 - 0.5) \] Calculating the coefficients of $d$: \[ -5.1 - 2 + 2.5 = -4.6 \] And for the constant terms: \[ 4.8 - 0.5 = 4.3 \]

Step 3: Write the Simplified Expression

Thus, the simplified expression is: \[ 4.3 - 4.6 d \]