Question

multiple-choice question
what like terms can be combined in this equation?
-9m and 18
-9m and 7m
18 and -10
there are no like terms.
rewatch

Explanation:

Like terms are terms with the same variable (or no variable for constants). For \(-9m\) and \(7m\), both have the variable \(m\), so they are like terms. \(-9m\) has a variable while \(18\) is a constant, so they aren't like terms. \(18\) and \(-10\) are constants (no variable), so they are also like terms. Wait, but let's re - check: The question is about which like terms can be combined. Let's analyze each option:

• Option 1: \(-9m\) (has \(m\)) and \(18\) (constant) are not like terms.
• Option 2: \(-9m\) and \(7m\) both have the variable \(m\) with the same power (power of 1), so they are like terms.
• Option 3: \(18\) and \(-10\) are both constants (no variable), so they are like terms.

But maybe the original equation (even though not fully shown) has these terms. Wait, the options are given. Let's see the standard definition: Like terms are terms that have the same variables raised to the same powers. So \(-9m\) and \(7m\) have the same variable \(m\) with exponent 1, so they are like terms. \(18\) and \(-10\) are both constants (no variables), so they are like terms too. But maybe in the context of the question (maybe the equation has \(-9m\), \(7m\), \(18\), \(-10\)), both \(-9m\) and \(7m\) (variable - like terms) and \(18\) and \(-10\) (constant - like terms) are like terms. But let's check the options again.

Wait, the options are:

• \(-9m\) and \(18\): Not like terms (one has \(m\), one is constant).
• \(-9m\) and \(7m\): Like terms (same variable \(m\)).
• \(18\) and \(-10\): Like terms (both constants).
• There are no like terms: Incorrect.

But maybe the question is from a context where the equation has these terms, and we need to pick the correct like - term pairs. Let's assume that the question is expecting the variable - like terms and constant - like terms. But let's check the options. If we have to choose the correct ones:

For \(-9m\) and \(7m\): They are like terms because they have the same variable \(m\) with the same exponent (1). For \(18\) and \(-10\): They are like terms because they are both constants (no variables).

But maybe the question has a typo or the equation is such that both \(-9m\) and \(7m\) and \(18\) and \(-10\) are like terms. But let's check the options again. The options are presented as checkboxes, so maybe multiple correct answers. But let's go by the definition:

Like terms can be:

• Terms with the same variable(s) and same exponents: \(-9m\) and \(7m\) fit this.
• Constant terms (terms without variables): \(18\) and \(-10\) fit this.

But maybe in the given question, the intended answers are \(-9m\) and \(7m\) (since they are variable - like terms) and \(18\) and \(-10\) (constant - like terms). But let's check the options again.

Wait, the user's question is a multiple - choice question. Let's list the correct options:

Answer:

B. \(-9m\) and \(7m\), C. \(18\) and \(-10\)

Wait, but the options are:

• \(-9m\) and \(18\)
• \(-9m\) and \(7m\)
• \(18\) and \(-10\)
• There are no like terms

So the correct options are the second (\(-9m\) and \(7m\)) and the third (\(18\) and \(-10\)) because:

• \(-9m\) and \(7m\): Same variable \(m\), so like terms.
• \(18\) and \(-10\): Both constants, so like terms.