Question

modeling with algebra tiles
drag tiles to the board to represent the expression.
board sum: 0
reset
use algebra tiles to model the expression, and then combine like terms. check all that apply.
3 + 2 + x + x
combine the x tiles and the integer tiles.
combine all the tiles.
the equivalent expression is 5 + 2x.
the equivalent expression is 7x.
use substitution to verify the expressions are equivalent.

Explanation:

Step1: Analyze the expression

The given expression is \(3 + 2 + x + x\). First, identify like terms: the constant terms (3 and 2) and the \(x\)-terms (\(x\) and \(x\)).

Step2: Combine constant terms

Combine \(3\) and \(2\): \(3 + 2 = 5\).

Step3: Combine \(x\)-terms

Combine \(x\) and \(x\): \(x + x = 2x\).

Step4: Form the equivalent expression

The combined expression is \(5 + 2x\). Now check the options:

• "Combine the \(x\) tiles and the integer tiles": Correct, as we combine \(x\)-terms and constant terms.
• "The equivalent expression is \(5 + 2x\)": Correct, from combining like terms.
• "Use substitution to verify...": Correct, substitution (e.g., let \(x = 1\), original: \(3+2+1+1 = 7\), equivalent: \(5 + 2(1)=7\)) works.
• "Combine all the tiles": Not accurate, we combine like terms (separate constants and \(x\)-terms), not all tiles together.
• "The equivalent expression is \(7x\)": Incorrect, as \(3 + 2 + x + x = 5 + 2x

eq 7x\).

Answer:

• Combine the \(x\) tiles and the integer tiles
• The equivalent expression is \(5 + 2x\)
• Use substitution to verify the expressions are equivalent