Property.
Section 1
Concept: Adding Linear Expressions
To add linear expressions, we remove parentheses and combine like terms.
Like terms have the same variable with the same exponent.
For linear expressions, we combine constant terms together and variable terms with the same variable together.
To add like terms, we add their numerical coefficients.
Section 2
Subtracting Equations and Distributing Negatives
When a variable in both equations has the exact same coefficient (e.g., and ), adding the equations will not eliminate it. Instead, you must subtract the entire second equation from the first.
To do this correctly, you must distribute the negative sign to every single term in the bottom equation (changing all their signs) and then add the equations together.
Write it out: .
Distribute the minus sign to flip the signs inside: .
Combine like terms: .
Since the terms are identical (), subtract the entire bottom equation:
Now add this to the top equation:
.
Back-substitute: .
Subtracting an entire equation is exactly the same as multiplying it by -1 and then adding. The most common mistake in algebra is subtracting the first term but forgetting to subtract the rest! To avoid this trap, do not try to subtract in your head. Physically draw parentheses around the bottom equation, write a minus sign outside, and rewrite the equation with every single sign flipped. Then, just add them normally.
Section 3
Subtracting Expressions with Rational Coefficients
To subtract expressions with rational coefficients, apply the same properties as with integers.
Distribute the negative sign to each term in the expression being subtracted, then combine like terms using the rules for adding and subtracting fractions and decimals.
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Section 1
Concept: Adding Linear Expressions
To add linear expressions, we remove parentheses and combine like terms.
Like terms have the same variable with the same exponent.
For linear expressions, we combine constant terms together and variable terms with the same variable together.
To add like terms, we add their numerical coefficients.
Section 2
Subtracting Equations and Distributing Negatives
When a variable in both equations has the exact same coefficient (e.g., and ), adding the equations will not eliminate it. Instead, you must subtract the entire second equation from the first.
To do this correctly, you must distribute the negative sign to every single term in the bottom equation (changing all their signs) and then add the equations together.
Write it out: .
Distribute the minus sign to flip the signs inside: .
Combine like terms: .
Since the terms are identical (), subtract the entire bottom equation:
Now add this to the top equation:
.
Back-substitute: .
Subtracting an entire equation is exactly the same as multiplying it by -1 and then adding. The most common mistake in algebra is subtracting the first term but forgetting to subtract the rest! To avoid this trap, do not try to subtract in your head. Physically draw parentheses around the bottom equation, write a minus sign outside, and rewrite the equation with every single sign flipped. Then, just add them normally.
Section 3
Subtracting Expressions with Rational Coefficients
To subtract expressions with rational coefficients, apply the same properties as with integers.
Distribute the negative sign to each term in the expression being subtracted, then combine like terms using the rules for adding and subtracting fractions and decimals.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter