Question

1. identify the terms, coefficients, and constants in this expression: 7y - 3 + 4y

Explanation:

Step1: Simplify the expression (combine like terms)

First, we combine the like terms \(7y\) and \(4y\). The expression \(7y - 3 + 4y\) can be rewritten as \((7y + 4y)-3\). Combining the coefficients of \(y\), we get \(7 + 4 = 11\), so the simplified expression is \(11y-3\). But we can also analyze the original expression without simplifying first for terms, coefficients, and constants.

Step2: Identify terms

In an algebraic expression, terms are the parts separated by addition or subtraction. For the expression \(7y - 3 + 4y\), we can rewrite the subtraction as addition of the opposite: \(7y+(- 3)+4y\). So the terms are \(7y\), \(-3\) (or \( - 3\) can be thought of as \(+(-3)\)), and \(4y\). Alternatively, after combining like terms, the terms of \(11y - 3\) are \(11y\) and \(-3\), but since we can consider the original non - combined terms, the terms in \(7y-3 + 4y\) are \(7y\), \(-3\), and \(4y\).

Step3: Identify coefficients

A coefficient is the numerical factor of a term with a variable. For the term \(7y\), the coefficient is \(7\); for the term \(4y\), the coefficient is \(4\) (and for the combined term \(11y\), the coefficient is \(11\), but from the original terms, we have coefficients \(7\) and \(4\)).

Step4: Identify constants

A constant term is a term without a variable. In the expression \(7y-3 + 4y\), the constant term is \(-3\) (because it does not have a variable attached to it).

Answer:

• Terms: \(7y\), \(-3\), \(4y\) (or if we combine like terms first, the terms are \(11y\) and \(-3\))
• Coefficients: \(7\), \(4\) (or \(11\) if we consider the combined like - term)
• Constant: \(-3\)