Question

write an expression that is equivalent to $-7 + 5d + 9 + (-2d)$.
identify the constant terms and variable terms.
constant terms variable terms
$-7$

Explanation:

Step1: Identify Constant Terms

Constant terms are terms without variables. In the expression \(-7 + 5d + 9 + (-2d)\), the constant terms are \(-7\) and \(9\) because they have no variable (like \(d\)) attached.

Step2: Identify Variable Terms

Variable terms are terms with variables. In the expression, the variable terms are \(5d\) and \(-2d\) because they have the variable \(d\).

To simplify the expression:

Step3: Combine Constant Terms

Combine \(-7\) and \(9\): \(-7 + 9 = 2\)

Step4: Combine Variable Terms

Combine \(5d\) and \(-2d\): \(5d + (-2d)=5d - 2d = 3d\)

Step5: Write the Equivalent Expression

Combine the results from Step3 and Step4: \(2 + 3d\) (or \(3d + 2\))

Answer:

Constant Terms: \(-7, 9\)

Variable Terms: \(5d, -2d\)

Equivalent Expression: \(3d + 2\) (or \(2 + 3d\))