Question

2.
maria represented the perimeter of the rectangle with the expression:
12x−612x - 612x−6
determine if marias expression is equivalent to carloss expression.
justify your reasoning.

Explanation:

Step1: Analyze Maria's expression

Maria's expression seems to have a typo. Assuming it's \(12x - 6+12x - 6+12x - 6\) (maybe a formatting error), combine like terms: \( (12x + 12x + 12x)+(-6-6-6)=36x - 18\). But since Carlos's expression isn't given, we can't fully determine. However, if we assume Maria's intended expression was simplifying, first, correct the expression (assuming repetition error, maybe \(12x - 6\) repeated? If it's \(12x - 6 + 12x - 6+12x - 6\), combine \(x\) terms: \(12x+12x + 12x = 36x\), constants: \(-6-6 - 6=-18\), so \(36x - 18\). But without Carlos's expression, we note the original Maria's expression as written (\(12x - 612x - 612x - 6\)) has a typo. Correcting the \(x\) terms: \(12x-612x-612x= (12 - 612 - 612)x=-1212x\), so expression is \(-1212x - 6\). But likely a formatting mistake (maybe three terms of \(12x - 6\)). To check equivalence, we need Carlos's expression, but the key is to simplify Maria's expression by combining like terms.

Step2: Combine like terms (assuming typo)

If Maria's expression is \(12x - 6+12x - 6+12x - 6\) (three times \(12x - 6\)), then:

• Combine \(x\) terms: \(12x+12x + 12x = 36x\)
• Combine constant terms: \(-6-6 - 6=-18\)
• So simplified: \(36x - 18\) or factor: \(18(2x - 1)\) or \(3(12x - 6)\) (if original was three \(12x - 6\) terms). But without Carlos's expression, we can only simplify Maria's (corrected) expression. If the original is \(12x - 612x - 612x - 6\), then \(x\) terms: \(12x-612x-612x=(12 - 612 - 612)x=-1212x\), constants: \(-6\), so \(-1212x - 6\), which is different from a proper perimeter (perimeter of rectangle is \(2(l + w)\), so should have two length and two width terms, sum to linear in \(x\) with two constant terms, not three. So likely a typo in the problem, but the process is to combine like terms in Maria's expression to check equivalence with Carlos's (unknown here, but the method is combining like terms).

Answer:

To determine equivalence, simplify Maria's expression (correcting the typo, e.g., if \(12x - 6\) repeated three times: \(3(12x - 6)=36x - 18\)). Without Carlos's expression, we can't fully conclude, but the key step is combining like terms in Maria's expression. If Carlos's expression matches the simplified form, they are equivalent; otherwise, not. (Note: The problem likely has a typo in Maria's expression, e.g., intended as \(12x - 6 + 12x - 6\) (perimeter of rectangle: \(2(l + w)\), so two length and two width terms), then \(24x - 12\), or three terms was a mistake. Assuming two terms: \(12x - 6+12x - 6 = 24x - 12 = 12(2x - 1)\), which is a valid perimeter expression. The equivalence depends on Carlos's expression, but the process is simplifying by combining like terms.)