Variables and Algebraic Expressions: Only addition and subtraction

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 $\boxed{19 + 3x}$.

To simplify the expression $5 + 0 + 8x - 5$, follow these steps:

• Step 1: Identify and group like terms. In this case, there are constants (5, 0, -5) and a term with a variable (8x).
• Step 2: Combine the constants: $5 + 0 - 5$.
• Step 3: Calculate: $5 - 5 = 0$.

Now, our expression simplifies to $0 + 8x$, which is simply $8x$.

Therefore, the simplified expression is $8x$.

To solve this problem, we will simplify the expression $5+8-9+5x-4x$ by separately combining the constants and the variable terms.

Step 1: Simplify the constant terms.
$5 + 8 - 9 = 4$

Step 2: Simplify the variable terms.
$5x - 4x = x$

Step 3: Combine the results from steps 1 and 2.
Thus, the simplified expression is $4 + x$.

Therefore, the solution to the problem is $4 + x$, which corresponds to choice .

To solve this algebraic problem, follow these steps:

• Step 1: Identify the coefficients of the variable $x$ in the expression $x + x$. Here, the coefficient for each $x$ is 1.
• Step 2: Add the coefficients together. This gives $1 + 1 = 2$.
• Step 3: Multiply the result by the variable. This results in $2x$.

Since the problem is a multiple-choice question, review the available choices to select the correct answer. The expression simplifies to $2x$, which corresponds to choice 3: $2x$.

Therefore, the solution to the problem is $2x$.

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 each given expression.
• Step 2: Compare the simplified expressions to determine if they are equivalent.

Now, let's work through each step:

Step 1: Simplify the expressions

First expression: $15x - 30$

• The expression is already simplified as it includes one variable term $15x$ and one constant term $-30$.

Second expression: $45 - 15 - 5x + 15x$

• Combine the constants: $45 - 15 = 30$.
• Combine the variable terms: $-5x + 15x = 10x$.
• The simplified form of the second expression is: $10x + 30$.

Step 2: Compare the simplified expressions

After simplification:

The first expression is $15x - 30$.

The second expression is $10x + 30$.

Clearly, these simplified expressions are not the same.

Therefore, the solution to the problem is No.