Working with Negative Coefficients
When solving equations with a negative sign outside parentheses in 8th grade algebra, the negative must be distributed to every term inside, not just the first. For 15 - (3x + 2) = 4x: distribute to get 15 - 3x - 2 = 4x, simplify to 13 - 3x = 4x, then 13 = 7x, so x = 13/7. For 5y = -2(y - 7): distribute to get 5y = -2y + 14, so 7y = 14, y = 2. This precision with negative distribution from enVision Mathematics, Grade 8, Chapter 2 prevents one of the most common equation-solving errors in 8th grade math.
Key Concepts
When a negative sign is in front of a parenthesis, it must be distributed to every term inside, changing the sign of each term. $$ (a + b) = a b$$ $$ (a b) = a + b$$.
Common Questions
How do I distribute a negative sign outside parentheses?
Multiply every term inside the parentheses by -1, changing the sign of each term. For -(3x + 2), the result is -3x - 2.
Solve 15 - (3x + 2) = 4x.
Distribute the negative: 15 - 3x - 2 = 4x. Simplify: 13 - 3x = 4x. Add 3x: 13 = 7x. Divide: x = 13/7.
Solve 5y = -2(y - 7).
Distribute -2: 5y = -2y + 14. Add 2y: 7y = 14. Divide: y = 2.
What is the most common mistake with negative distribution?
Only changing the sign of the first term inside the parentheses. For -(3x + 2), incorrectly writing -3x + 2 instead of -3x - 2.
What does subtracting a negative term equal?
Subtracting a negative equals adding the positive. For example, 5x - (-2x) = 5x + 2x = 7x.
When do 8th graders learn about negative coefficients in equations?
Chapter 2 of enVision Mathematics, Grade 8 covers this in the Analyze and Solve Linear Equations unit.