Variables and Algebraic Expressions Practice Problems

To determine if the expressions $18x$ and $2 + 9x$ are equivalent, we'll analyze their structures.

• $18x$ is a linear expression with a single term involving the variable $x$, and its coefficient is 18.
• $2 + 9x$ consists of two terms: a constant term $2$ and a linear term $9x$ with coefficient 9.

For two expressions to be equivalent, each corresponding term must be equal. Here, the expression $18x$ has no constant term, whereas $2 + 9x$ has a constant term of 2. Furthermore, the linear term coefficients differ: $18 \neq 9$.

Therefore, the expressions $18x$ and $2 + 9x$ are not the same. They structurally differ and cannot be made equivalent just through similar values of $x$.

Therefore, the solution to this problem is: No.

To solve this problem, we'll follow these steps:

• Step 1: Simplify the expression $2 \times 10x$.
• Step 2: Compare the simplified expression with $20x$.

Now, let's work through each step:
Step 1: The expression $2 \times 10x$ can be rewritten using associativity as $2 \times (10 \times x)$.
Step 2: Apply the associative property of multiplication: $(2 \times 10) \times x = 20 \times x = 20x$.

Comparing this with the given expression, we see that both expressions are indeed the same, as they simplify to $20x$.

Therefore, the solution to the problem is Yes.

To solve this problem, we'll analyze the expressions $3+3+3+3$ and $3 \times 4$ to determine if they are equivalent.

First, evaluate the expression $3+3+3+3$:

• Add the numbers: $3 + 3 = 6$
• Add again: $6 + 3 = 9$
• Add the last $3$: $9 + 3 = 12$

The result of $3+3+3+3$ is $12$.

Next, evaluate the expression $3 \times 4$:

• Perform the multiplication: $3 \times 4 = 12$

The result of $3 \times 4$ is also $12$.

Since both expressions result in the same number, we conclude that

The expressions are the same.

Therefore, the correct answer is Yes.

To solve this problem, we'll follow these steps:

• Step 1: Identify the like terms in the expression.
• Step 2: Combine the constant terms.
• Step 3: Combine the coefficients of $x$.

Now, let's work through each step:
Step 1: The given expression is $11 + 5x - 2x + 8$. There are constants (11 and 8) and terms with $x$ (5x and -2x).
Step 2: Combine the constants: $11 + 8 = 19$.
Step 3: Combine the coefficients of $x$: $5x - 2x = 3x$.

After simplification, the expression becomes $19 + 3x$.

The correct solution from the multiple-choice options is $\boxed{19 + 3x}$.

Let's simplify the expression $3x + 4x + 7 + 2$ step-by-step:

• Step 1: Combine Like Terms Involving $x$
  The terms $3x$ and $4x$ are like terms because both involve the variable $x$. To combine them, add their coefficients:
  $3x + 4x = (3 + 4)x = 7x$

• Step 2: Combine Constant Terms
  The expression includes constant terms $7$ and $2$. These can be added together to simplify:
  $7 + 2 = 9$

• Step 3: Write the Simplified Expression
  Now, combine the results from Step 1 and Step 2 to form the final simplified expression:
  $7x + 9$

Therefore, the simplified expression is $7x + 9$.

Reviewing the choices provided, the correct choice is:

• Choice 2: $7x + 9$

This matches our simplified expression, confirming our solution is correct.