Add and subtract algebraic expressions unit 4, lesson 6
In Unit 4, Lesson 6, you will learn how to add and subtract algebraic expressions. Here are the steps you need to follow:
Step 1: Simplify each expression separately: If there are any like terms, you can combine them by adding or subtracting their coefficients.
Step 2: Identify the common terms: Look for any terms that are exactly the same in both expressions.
Step 3: Determine the sign: To add or subtract the expressions, you need to consider the sign of each term. If the common term has a positive coefficient in both expressions, you add them. If it has a negative coefficient in one expression, you subtract them.
Step 4: Combine the terms: Add or subtract the coefficients of the common terms.
Step 5: Write the final expression: Combine the simplified terms and the terms with common coefficients.
For example, let's say we have the expressions 3x + 2y - 4z and -2x + 5y + 3z.
Step 1: Simplify each expression:
3x + 2y - 4z remains the same.
-2x + 5y + 3z remains the same.
Step 2: Identify the common terms:
In this example, there are no common terms.
Step 3: Determine the sign:
All terms have positive coefficients in both expressions, so we add them together.
Step 4: Combine the terms:
(3x + -2x) + (2y + 5y) + (-4z + 3z) simplifies to x + 7y - z.
Step 5: Write the final expression:
The final expression is x + 7y - z.
So, in Unit 4, Lesson 6, you will learn how to add and subtract algebraic expressions by combining like terms and considering the sign of each term.
9(k+1/3)+10(1/2k-1)
To add or subtract the given algebraic expressions, we need to perform the following steps:
Step 1: Simplify each expression separately: Distribute the coefficients to the terms inside the parentheses.
9(k + 1/3) + 10(1/2k - 1)
Expanding the first expression: 9k + 9/3
Expanding the second expression: 10/2k - 10
Step 2: Identify the common terms: In this case, there are no common terms.
Step 3: Determine the sign: Since there are no common terms, we don't need to consider any signs.
Step 4: Combine the terms: Since there are no common terms, we can't combine them.
Step 5: Write the final expression: The final expression remains as it is.
Therefore, the final expression is:
9(k + 1/3) + 10(1/2k - 1) = 9k + 9/3 + 10/2k - 10
To add or subtract algebraic expressions, follow these steps:
Step 1: Group like terms
Identify the like terms in the expression. These are the terms that have the same variables raised to the same powers.
Step 2: Add or subtract the coefficients
For each group of like terms, add or subtract their coefficients (numbers in front of the variables).
Step 3: Keep the variable term
Keep the variable term the same. It should have the same variables and exponents.
Step 4: Combine like terms
Combine the coefficients and keep the variable terms.
Step 5: Simplify the result
If possible, simplify the expression further by combining like terms or performing any necessary operations.
Here's an example to illustrate the steps:
Example:
Let's add the algebraic expressions 3x + 2y - 5 and 2x - 3y + 4.
Step 1: Group like terms
3x and 2x are like terms.
2y and -3y are like terms.
Step 2: Add or subtract the coefficients
3x + 2x = 5x
2y - 3y = -y
Step 3: Keep the variable term
Both 5x and -y have the same variable terms.
Step 4: Combine like terms
Combine 5x and -y to get 5x - y.
Step 5: Simplify the result
The final result is 5x - y.
This is how you add and subtract algebraic expressions step-by-step.
To add and subtract algebraic expressions, you need to follow a few steps:
1. Identify like terms: Like terms are expressions that have the same variables raised to the same powers. For example, 2x, -3x, and 5x are like terms because they all have the variable x raised to the power 1. On the other hand, 2x^2 and 3x^2 are not like terms because they have the same variable x raised to different powers.
2. Combine like terms: To add or subtract expressions, you can only combine like terms. This means you can add or subtract the coefficients (the numbers in front of the variable) while keeping the variable and its power the same.
3. Simplify the expression: After combining the like terms, you can simplify the expression by collecting similar terms. If the variable is missing in some terms, you can treat it as having a coefficient of zero.
Example:
Let's say we have the following expression:
2x + 3y - 5x - 4y
First, identify the like terms: 2x and -5x are like terms because they have the same variable x raised to the power 1. Similarly, 3y and -4y are like terms because they have the same variable y raised to the power 1.
Next, combine the like terms: 2x - 5x = -3x, and 3y - 4y = -y.
So, the simplified expression becomes:
-3x - y
This is how you add and subtract algebraic expressions by combining like terms.