Problem 56 Subtract. $$\begin{array}{r} ... [FREE SOLUTION]

Chapter 6: Problem 56

Subtract. $$\begin{array}{r} 10 q-7 \\ -\quad 4 q+8 \\ \hline \end{array}$$

Short Answer

Expert verified

The short answer is: $6q - 15$

Step by step solution

Subtract the variable parts

Begin by subtracting the variable parts of the expressions. In this case, we have $10q - 4q$. Subtracting these, we get: $10q - 4q = 6q$

Subtract the constant parts

Now let's subtract the constant parts of the expressions. We have $-7 - 8$. Subtracting these, we get: $-7 - 8 = -15$

Combine the results

Finally, combine the results from Steps 1 and 2. We have: $6q - 15$ So, the result of subtracting the given expressions is $6q - 15$.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Subtraction

Subtraction is an arithmetic operation used to find the difference between two numbers or expressions. In algebra, it's important because it helps us simplify expressions and solve equations.
Let's consider the subtraction of two expressions, like in our example.

The focus is to subtract one full expression from another. This involves considering both the variable and constant parts separately.
You perform the subtraction by lining up similar terms: variables line up with variables, and constants line up with constants.

When subtracting, remember to distribute the negative sign to each element in the expression being subtracted.

Variable Parts

When we refer to variable parts in an expression, we talk about the components that contain variables. In our example, the variable part includes terms with 'q'.
Here鈥檚 how you handle the subtraction of variable parts:

Identify terms with the same variable across the expressions. In this case, it's '10q' and '4q'.
Subtract these terms: you do this by subtracting their coefficients (10 and 4) while the variable remains the same.
Thus, '10q - 4q' results in '6q'.

Always ensure you're subtracting coefficients correctly and that you keep the variables unchanged.

Constant Parts

Constant parts in an expression are numbers without a variable factor. They remain the same no matter what the variable's value is. In algebra, subtracting constant parts follows regular arithmetic rules.
For our exercise, consider the following steps:

Identify the constants in each expression. Here, we have '-7' and '8'.
Subtract them by calculating $-7 - 8$, which equals $-15$.

Handling constants is simpler as no variables are involved; it's straightforward arithmetic subtraction, but remember the effect of negative signs.

Step-by-Step Solution

Breaking down a problem into simple steps makes solving it easier to understand. Here is how you can approach subtracting algebraic expressions:

Step 1: Focus on the variable parts first. Line them up and subtract their coefficients. For example, subtracting '4q' from '10q' gives '6q'.
Step 2: Next, look at the constant parts. Subtract the numbers directly, like '-7' from '8', resulting in '-15'.
Step 3: Combine the outcomes of the previous steps into a single expression, which gives you the result '6q - 15'.

Following these consistent steps helps ensure a correct and understandable outcome in algebra, reinforcing the principles at each stage.

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91影视

Subtract. $$\begin{array}{r} 10 q-7 \\ -\quad 4 q+8 \\ \hline \end{array}$$

Short Answer

Step by step solution

Subtract the variable parts

Subtract the constant parts

Combine the results

Key Concepts

Subtraction

Variable Parts

Constant Parts

Step-by-Step Solution

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