Question

combining like terms
combine like terms to write an equivalent expression. then complete the statements.
2f + 5 + f - 3
the constants, , are like terms.
are also like terms.
combine the constant terms by .
combine the variable terms by adding the .
the equivalent expression is .

Explanation:

Step1: Identify like terms

In the expression \(2f + 5 + f - 3\), the variable terms \(2f\) and \(f\) are like terms (both have the variable \(f\)), and the constant terms \(5\) and \(-3\) are like terms (both are constants).

Step2: Combine variable terms

Add the coefficients of the variable terms: \(2f + f=(2 + 1)f = 3f\).

Step3: Combine constant terms

Add the constant terms: \(5-3 = 2\).

Step4: Form equivalent expression

Combine the results from Step2 and Step3: \(3f+2\).

Answer:

• The variable terms \(2f\) and \(f\) are like terms. The constant terms \(5\) and \(-3\) are like terms.
• Combine the constant terms by adding \(5\) and \(-3\) (resulting in \(2\)).
• Combine the variable terms by adding the coefficients \(2\) and \(1\) (resulting in \(3f\)).
• The equivalent expression is \(3f + 2\).