Question

which represent like terms in the model of the equation?

a: two green tiles labeled x and three orange tiles labeled 1
b: two green tiles labeled x and three green tiles labeled x

Explanation:

🆕 New Concept Discovered: Identifying Like Terms
Terms with the exact same variables.

Step 1: Identify the terms in the model

The model represents an equation using algebra tiles:

• On the left side, we have two green tiles labeled \(x\) and three yellow tiles labeled \(1\). This represents the expression:

$$ 2x + 3 $$

• On the right side, we have three green tiles labeled \(x\). This represents the expression:

$$ 3x $$

The full equation modeled is:

$$ 2x + 3 = 3x $$

Step 2: Define like terms

Like terms are terms in an algebraic expression or equation that have the exact same variable parts raised to the same powers.

• The terms containing \(x\) (the green tiles) are like terms because they both have the variable \(x\).
• The constant terms (the yellow tiles labeled \(1\)) are not like terms with the \(x\) terms because they do not contain the variable \(x\).

Step 3: Match with the given options

We need to find which option shows groups of tiles that represent like terms:

• Option A shows the green \(x\) tiles and the yellow \(1\) tiles. These are unlike terms because one group represents variables (\(2x\)) and the other represents constants (\(3\)).
• Option B shows the two green \(x\) tiles (\(2x\)) and the three green \(x\) tiles (\(3x\)). These are like terms because both groups represent terms with the same variable, \(x\).

Therefore, Option B represents the like terms in the model.

Answer:

B (the option showing the two green \(x\) tiles and the three green \(x\) tiles)