Question

which terms are like terms in the expression (6a + 9 + (-7a))? choose all that apply.
options: (6a), (9), (-7a)

Explanation:

Step1: Identify like terms

Like terms are terms with the same variable (or no variable for constant terms) raised to the same power. In the expression \(6a + 9+(-7a)\), we can rewrite it as \(6a + 9 - 7a\). The terms with the variable \(a\) are \(6a\) and \(-7a\). The constant term is \(9\), and there's no other term with just a constant (other than 9) or a different variable. So we check each option:
- For \(6a\): It has the variable \(a\), same as \(-7a\) (since \(-7a\) also has \(a\)), so they are like terms.
- For \(9\): It's a constant term, and there's no other constant term in the expression to be like with (the other terms have \(a\)), so 9 is not a like term with \(6a\) or \(-7a\) (since those have \(a\)). Wait, no—wait, the question is "Which terms are like terms in the expression \(6a + 9+(-7a)\)? Choose ALL that apply." Wait, maybe I misread. Wait, the terms are \(6a\), \(9\), and \(-7a\). Like terms are terms with the same variable part. So \(6a\) and \(-7a\) have the same variable \(a\) (same exponent, which is 1), so they are like terms. \(9\) is a constant, so it's only like with other constants, but there are none here. Wait, but the options are \(6a\), \(9\), \(-7a\). Wait, maybe the question is which terms are like terms among these three. So \(6a\) and \(-7a\) are like terms because they have the same variable \(a\) with exponent 1. \(9\) is a constant, so it's not like with \(6a\) or \(-7a\). Wait, but let's re-express the expression: \(6a + 9 - 7a\). Combining like terms: \( (6a - 7a) + 9 = -a + 9\). So the like terms are \(6a\) and \(-7a\). Wait, but the options are \(6a\), \(9\), \(-7a\). So we need to check which of these are like terms. So \(6a\) and \(-7a\) are like terms (same variable, same exponent). \(9\) is a constant, so it's not like with \(6a\) or \(-7a\) (since those have \(a\)). Wait, maybe the question is a bit different—maybe a typo? Wait, no, let's check again. The expression is \(6a + 9 + (-7a)\), which is \(6a + 9 - 7a\). The terms are \(6a\) (term 1), \(9\) (term 2), \(-7a\) (term 3). Like terms are terms with identical variable parts. So term 1 (\(6a\)) and term 3 (\(-7a\)) have the same variable \(a\) (exponent 1), so they are like terms. Term 2 (\(9\)) is a constant, so it's not like with the others. So the like terms are \(6a\) and \(-7a\). Wait, but the options are \(6a\), \(9\), \(-7a\). So we need to select \(6a\) and \(-7a\) as the like terms. Wait, maybe I made a mistake. Wait, no—like terms are terms that can be combined because they have the same variable (or no variable, for constants) with the same exponent. So \(6a\) and \(-7a\) have the variable \(a\) with exponent 1, so they are like terms. \(9\) is a constant, so it's only like with other constants, but there are none here. So the like terms are \(6a\) and \(-7a\). Wait, but the options are \(6a\), \(9\), \(-7a\). So we need to choose \(6a\) and \(-7a\) (and maybe \(9\) is not, but wait, maybe the question is phrased differently. Wait, maybe the original problem is "Which terms are like terms in the expression \(6a + 9 + (-7a)\)? Choose ALL that apply." So the terms are \(6a\), \(9\), \(-7a\). So \(6a\) and \(-7a\) are like terms (same variable \(a\), same power). \(9\) is a constant, so it's not like with \(6a\) or \(-7a\). So the correct like terms are \(6a\) and \(-7a\). Wait, but let's check the options again. The options are \(6a\), \(9\), \(-7a\). So we need to select \(6a\) and \(-7a\). Wait, maybe I misread the expression. Let me confirm: the expression is \(6a + 9 + (-7a)\), which is \(6a + 9 - 7a\). So terms: \(6a\) (variable term), \(9\) (constant term), \(-7a\) (variable term). So variable terms with \(a\) are \(6a\) and \(-7a\), so they are like terms. Constant term is \(9\), no other constant term. So the like terms are \(6a\) and \(-7a\). So among the options, \(6a\) and \(-7a\) are like terms. \(9\) is not a like term with them because it has no variable.

Wait, but maybe the question is asking which terms are like terms, so we need to pick all pairs? But the options are individual terms. Wait, maybe the question is "Which of these terms are like terms (i.e., which terms can be combined)?", so \(6a\) and \(-7a\) are like terms, so we select \(6a\) and \(-7a\). \(9\) is not a like term with them. So the answer should be \(6a\) and \(-7a\).

Answer:

\(6a\), \(-7a\)