Javier used the expression below to represent his score in a game of mini-golf.

$3x + x + 5 - 2x$

If he simplifies the expression, which statements are true about the parts of the simplified expression? Select three options.

The constant is 2.
The coefficient is 2.
The constant is 5.
The coefficient is 5.
There are two terms.

Question

31-10-2026
Mathematics

Answered

Javier used the expression below to represent his score in a game of mini-golf.

$3x + x + 5 - 2x$

If he simplifies the expression, which statements are true about the parts of the simplified expression? Select three options.

The constant is 2.
The coefficient is 2.
The constant is 5.
The coefficient is 5.
There are two terms.

Verified Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-10-31T13:23:08-04:00

Simplify the expression by combining the coefficients of like terms: $3x + x - 2x = 2x$.
The resulting simplified expression is $2x + 5$.
Identify that the coefficient of the variable term is $2$, the constant term is $5$, and there are two terms in the expression.
The three true statements are: $\boxed{\text{The coefficient is 2, The constant is 5, There are two terms.}}$

Explanation

Simplifying the Expression

The expression given for Javier's score is $3x + x + 5 - 2x$. To simplify this, we identify the like terms. The like terms are those that contain the variable $x$: $3x$, $x$, and $-2x$. The constant term is 5. Combining the coefficients of the $x$ terms, we have:
\[ (3 + 1 - 2)x + 5 \]
Calculating the sum of the coefficients: $3 + 1 = 4$ and $4 - 2 = 2$.
Thus, the simplified expression is:
\[ 2x + 5 \]

Analyzing the Simplified Expression

Now that we have the simplified expression $2x + 5$, we can analyze its components:

The coefficient is the numerical factor multiplying the variable $x$, which is $2$.
The constant is the term without a variable, which is $5$.
The expression $2x + 5$ consists of two separate terms: $2x$ and $5$.

Comparing these findings with the provided options:

"The constant is 2" is False.
"The coefficient is 2" is True.
"The constant is 5" is True.
"The coefficient is 5" is False.
"There are two terms" is True.

The three true statements are: "The coefficient is 2", "The constant is 5", and "There are two terms".

Examples

In many real-world scenarios, we use variables to represent unknown or changing values. For example, if you rent a car for a base fee of \$@@MATH_TOKEN_22@@ plus \$$10$ for each hour driven, the total cost could be represented by the expression $10h + 50$. Simplifying expressions like this allows us to quickly identify the fixed costs (the constant) and the rate of change (the coefficient), helping us make better financial decisions. Similar logic applies to planning budgets, calculating manufacturing costs, or analyzing physics problems where variables change.