High School

Tyrone wrote an equivalent expression for [tex]28 + x + 2n + 7 + n + 5x + 4[/tex]. His equivalent expression was [tex]3n + 5x + 39 + x[/tex]. What error did Tyrone make?

A. Tyrone neglected to combine the [tex]x[/tex] terms.

B. Tyrone subtracted the constants instead of adding them.

C. Tyrone neglected to add the coefficients of the [tex]n[/tex] terms.

D. Tyrone made an error when he added the constants.

Answer :

To solve the problem and determine if Tyrone made an error in simplifying the expression, let's first look at the given original expression and simplify it ourselves:

The original expression is:
[tex]\[ 28 + x + 2n + 7 + n + 5x + 4 \][/tex]

Step 1: Combine like terms.

- Combine the [tex]\(x\)[/tex] terms:
- [tex]\(x + 5x = 6x\)[/tex]

- Combine the [tex]\(n\)[/tex] terms:
- [tex]\(2n + n = 3n\)[/tex]

- Combine the constant terms:
- [tex]\(28 + 7 + 4 = 39\)[/tex]

So, the simplified form of the original expression is:
[tex]\[ 6x + 3n + 39 \][/tex]

Now, let's look at the expression that Tyrone gave:
[tex]\[ 3n + 5x + 39 + x \][/tex]

Step 2: Simplify Tyrone's expression to confirm equivalence.

- Combine the [tex]\(x\)[/tex] terms in Tyrone's expression:
- [tex]\(5x + x = 6x\)[/tex]

- The [tex]\(n\)[/tex] terms already appear as [tex]\(3n\)[/tex].

- The constant term is [tex]\(39\)[/tex].

Thus, Tyrone's expression simplifies to:
[tex]\[ 6x + 3n + 39 \][/tex]

Comparing both simplified versions, they are indeed the same:
- Both have [tex]\(6x + 3n + 39\)[/tex].

Conclusion: Tyrone did not make an error. His expression is equivalent to the original.