Variables and Algebraic Expressions: Applying the formula

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 simplify the expression $7a + 8b + 4a + 9b$, we will follow these steps:

• Step 1: Identify like terms. The expression contains terms involving $a$ ($7a$ and $4a$) and terms involving $b$ ($8b$ and $9b$).
• Step 2: Combine the coefficients of like terms.
• Step 3: Rewrite the simplified expression.

Step 1: The like terms involving $a$ are $7a$ and $4a$.

Step 2: Add these coefficients: $7 + 4 = 11$. Therefore, the combined term for $a$ is $11a$.

Step 3: The like terms involving $b$ are $8b$ and $9b$.

Step 4: Add these coefficients: $8 + 9 = 17$. Therefore, the combined term for $b$ is $17b$.

Thus, the expression simplifies to $11a + 17b$.

The correct answer choice is: $11a + 17b$.

To solve the exercise, we will reorder the numbers using the substitution property.

$18x-8x+4x-7-9=$

To continue, let's remember an important rule:

1. It is impossible to add or subtract numbers with variables.

That is, we cannot subtract 7 from 8X, for example...

We solve according to the order of arithmetic operations, from left to right:

$18x-8x=10x$$10x+4x=14x$$-7-9=-16$Remember, these two numbers cannot be added or subtracted, so the result is:

$14x-16$

To solve the problem, we should simplify the expression by combining like terms:

• Step 1: Identify like terms.
  • The terms involving $a$ are $13a$ and $-4a$.
  • The terms involving $b$ are $14b$, $-2b$, and $-4b$.
  • The term involving $c$ is $17c$.
• Step 2: Combine like terms by summing their coefficients:
  • For $a$-terms: $13a - 4a = (13 - 4)a = 9a$.
  • For $b$-terms: $14b - 2b - 4b = (14 - 2 - 4)b = 8b$.
  The $c$ term remains unchanged as $17c$.

Therefore, the simplified expression is $9a + 8b + 17c$.

Checking the choices provided, we see that the correct answer is $9a + 8b + 17c$, which matches choice .

Thus, the final simplified expression is $9a + 8b + 17c$.

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

• Step 1: Identify and group like terms.
• Step 2: Combine the coefficients for each type of term.

Let's begin the simplification process:

First, we identify and group the like terms in the expression $a + b + bc + 9a + 10b + 3c$.

Notice: - The terms involving $a$ are $a$ and $9a$. - The terms involving $b$ are $b$ and $10b$. - The terms involving $c$ are $3c$, and the multiplication term with $c$ is $bc$.

Step 2: Combine the like terms:

$a + 9a = 10a$

$b + 10b = 11b$

The term $bc$ can be rearranged with $3c$ as $(b+3)c$.

Thus, after combining the terms, we have:

$10a + 11b + (b + 3)c$.

Therefore, the simplified form of the expression is:

$10a + 11b + (b + 3)c$

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

• Identify and group like terms within the expression.
• Combine the coefficients of these like terms.
• Simplify the expression by adding or subtracting coefficients.

Now, let's work through each step:

Step 1: Observe the given algebraic expression:
    $35m + 9n - 48m + 52n$.

Step 2: Group like terms, separating terms with $m$ from those with $n$:
    $(35m - 48m)$ and $(9n + 52n)$.

Step 3: Combine the terms with $m$:
    $35m - 48m = (35 - 48)m = -13m$.

Step 4: Combine the terms with $n$:
    $9n + 52n = (9 + 52)n = 61n$.

Therefore, the simplified form of the expression is:
    $61n - 13m$.

This leads to our final solution:

$61n - 13m$

In order to solve this question, remember that we can perform the addition and subtraction operations when we have the same variable.
However we are limited when we have several different variables.
 

Note that in this exercise that we have three variables:
$45$ which has no variable
$8y$ and $34y$ which both have the variable $y$
and $45z$ with the variable $z$

Therefore, we can only operate with the y variable, since it's the only one that exists in more than one term.

Rearrange the exercise:

$45-34y+8y-45z$

Combine the relevant terms with $y$

$45-26y-45z$

We observe that this is similar to one of the other answers, with a small rearrangement of the terms:

$-26y+45-45z$

Given that we have no possibility to perform additional operations - this is the solution!

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

• Step 1: Identify the like terms in the expression.
• Step 2: Combine these like terms by adding their coefficients.

Now, let's work through each step:

Step 1: In the expression $5a + 3a + 8b + 10b$, we have two types of like terms:

• Terms involving $a$: $5a$ and $3a$.
• Terms involving $b$: $8b$ and $10b$.

Step 2: Combine like terms:

• For the terms involving $a$: Combine $5a + 3a$ to get $8a$.
• For the terms involving $b$: Combine $8b + 10b$ to get $18b$.

The simplified expression combining all the terms is $8a + 18b$.

Therefore, the solution to the problem is $8a + 18b$.

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

• Identify the terms involving the same variables.
• Combine like terms, particularly those involving $a$.
• Simplify the expression based on the calculations.

Now, let's work through each step:
Step 1: The given expression is $3.4 - 3.4a + 2.6b - 7.5a$.
Step 2: Identify the like terms:
- The terms with $a$ are $-3.4a$ and $-7.5a$.
Step 3: Combine these like terms:
- Calculate $-3.4a - 7.5a = (-3.4 - 7.5)a = -10.9a$.
Step 4: Substitute back into the expression:
- The simplified expression is $3.4 - 10.9a + 2.6b$.

Therefore, the solution to the problem is $3.4 - 10.9a + 2.6b$.

It is important to remember that when we have numbers and variables, it is impossible to add or subtract them from each other.

We group the elements:

$7.3×4a + 2.3 + 8a =$

29.2a + 2.3 + 8a = 

$37.2a + 2.3$

And in this exercise, this is the solution!

You can continue looking for the value of a.

But in this case, there is no need.

To solve this problem, we need to simplify the given expression:

1. Identify and group similar terms:

• Constant term: $7.8$
• Terms with $a$: $3.5a + 3.9a$
• Terms with $b$: $-80b - 7.8b$

2. Simplify each group:

• Combine terms with $a$:
  $3.5a + 3.9a = (3.5 + 3.9)a = 7.4a$
• Combine terms with $b$:
  $-80b - 7.8b = (-80 - 7.8)b = -87.8b$

3. The constant term remains $7.8$.

4. Therefore, the simplified expression is:
$7.8 + 7.4a - 87.8b$

Thus, the correct answer is $\boxed{7.8 + 7.4a - 87.8b}$

To solve the problem, we will simplify the expression $39.3 : 4a + 5a + 8.2 + 13z$. Let's break down the steps:

• Step 1: Simplify the division $39.3 : 4a$.
  To solve $39.3 : 4a$, we treat this as $\frac{39.3}{4a}$.
  Calculating the division: $\frac{39.3}{4} = 9.825$. Therefore, $\frac{39.3}{4a} = \frac{9.825}{a}$.
• Step 2: Rearrange the terms.
  We now have $\frac{9.825}{a} + 5a + 8.2 + 13z$. No like terms for direct combination exist as these are distinct variables and constants.
• Step 3: Write the expression.
  The terms should be written in a neat, arranged form as $13z + 8.2 + \frac{9.825}{a} + 5a$.

Therefore, the simplified expression is $\ 13z + 8.2 + \frac{9.825}{a} + 5a$.

To solve this problem, follow these steps:

• Step 1: Identify Like Terms

The expression is $5.6x + 7.9y + 53xy + 12.1x$. Here, $5.6x$ and $12.1x$ are like terms.

• Step 2: Combine Like Terms

Add the coefficients of $x$: $5.6x + 12.1x = (5.6 + 12.1)x = 17.7x$.

• Step 3: Write the Simplified Expression

After combining the like terms, we get:

$17.7x + 7.9y + 53xy$

This is the simplified form of the expression.

Therefore, the solution to the problem is $17.7x + 53xy + 7.9y$.

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

• Step 1: Combine like terms.
• Step 2: Simplify the expression.

Now, let's work through each step:
Step 1: Start by identifying and combining like terms in the expression $\frac{1}{4}a + \frac{1}{3}x + \frac{2}{4}a + \frac{1}{8} + \frac{3}{8}$. Recognize that $\frac{1}{4}a$ and $\frac{2}{4}a$ are like terms since they both involve the variable $a$.

Combine these terms:

$\frac{1}{4}a + \frac{2}{4}a = \frac{3}{4}a$

Step 2: Look at the constant terms $\frac{1}{8} + \frac{3}{8}$. Since these fractions have a common denominator, add them directly:

$\frac{1}{8} + \frac{3}{8} = \frac{4}{8} = \frac{1}{2}$

Combine all the terms together to form the simplified expression:

$\frac{3}{4}a + \frac{1}{3}x + \frac{1}{2}$

Therefore, the solution to the problem is $\frac{3}{4}a + \frac{1}{3}x + \frac{1}{2}$.

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

• Step 1: Group and simplify terms with the same variable.
• Step 2: Convert any mixed numbers to improper fractions.
• Step 3: Find a common denominator to combine fractions.
• Step 4: Simplify the expression.

Let's work through the steps:
Step 1: Start by grouping like terms. The expression is:
$\frac{3}{8}a + \frac{6}{8}a + \frac{14}{9}b + 1\frac{1}{9}b$.
Step 2: Convert the mixed number to an improper fraction. For $1\frac{1}{9}b$: $1\frac{1}{9}b = \frac{10}{9}b$.
Rewrite the expression: $\frac{3}{8}a + \frac{6}{8}a + \frac{14}{9}b + \frac{10}{9}b$.
Step 3: Combine the $a$-terms and $b$-terms separately:
The $a$-terms: $\frac{3}{8}a + \frac{6}{8}a = \left(\frac{3}{8} + \frac{6}{8}\right)a = \frac{9}{8}a$.
For the $b$-terms: $\frac{14}{9}b + \frac{10}{9}b = \left(\frac{14}{9} + \frac{10}{9}\right)b = \frac{24}{9}b$.
Simplify $\frac{24}{9}$: $\frac{24}{9} = \frac{8}{3}$ after dividing by the greatest common divisor 3.
Step 4: Combine simplified terms: $\frac{9}{8}a + \frac{8}{3}b$.
Convert $\frac{9}{8}a$ to a mixed number: $\frac{9}{8}a = 1\frac{1}{8}a$.
Convert $\frac{8}{3}b$ to a mixed number: $\frac{8}{3}b = 2\frac{2}{3}b$.
Thus, the simplified expression is: $1\frac{1}{8}a + 2\frac{2}{3}b$.

Therefore, the solution to the problem is $1\frac{1}{8}a + 2\frac{2}{3}b$.