Variables and Algebraic Expressions - Examples, Exercises and Solutions

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.

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

• Step 1: Combine like terms by identifying and adding their coefficients.
• Step 2: Simplify the expression.
• Step 3: Verify the resulting expression with the provided choices.

Let's work through each step:

Step 1: Identify the coefficients in the expression $3z + 19z - 4z$. The coefficients are $3$, $19$, and $-4$.

Step 2: Add and subtract these coefficients: $3 + 19 - 4$.

Step 3: Calculate: $3 + 19 = 22$ and then $22 - 4 = 18$.

Therefore, the simplified expression is $18z$.

The solution to the problem is $18z$.

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 .