Distributing a sneaky negative
Master distributing a sneaky negative sign in Grade 9 algebra by multiplying every term inside parentheses by -1, avoiding the common sign-flip error in Saxon Algebra 1.
Key Concepts
Property When distributing a negative sign across parentheses, remember to multiply each term inside by $ 1$. For example, $ (x 3)$ becomes $ 1 \cdot x + ( 1) \cdot ( 3)$, which simplifies to $ x + 3$.
Examples Solve $7x (x 4) 2 = 26$. Distribute the negative: $7x x + 4 2 = 26$. Combine terms: $6x + 2 = 26$. Solve: $6x = 24$, so $x = 4$. Simplify $15 (3y + 5)$. Distributing the negative gives $15 3y 5$. Combining the constants results in $10 3y$. Solve $ 4(b 5) = 32$. Distribute the $ 4$: $ 4b + 20 = 32$. Subtract 20: $ 4b = 12$. Divide by $ 4$: $b = 3$.
Explanation That sneaky negative sign outside a parenthesis is a master of disguise! It's not just subtracting the first term; it’s a ninja that flips the sign of every single term inside. Think of it as distributing a $ 1$ to everything. Forgetting to flip all the signs is a super common trap, so stay alert!
Common Questions
What does 'distributing a sneaky negative' mean in algebra?
When a negative sign appears outside parentheses, it must be multiplied (distributed) to every term inside, not just the first. For example, -(x - 3) becomes -x + 3 because -1 times -3 equals +3.
How do you solve 7x - (x - 4) - 2 = 26 using negative distribution?
Distribute the negative to get 7x - x + 4 - 2 = 26. Combine like terms to get 6x + 2 = 26, then solve to find x = 4. The key step is flipping the sign of every term inside the parentheses.
What is the most common mistake when distributing a negative sign?
Students often flip only the first term inside the parentheses and leave remaining terms unchanged. Always apply -1 to every single term inside the brackets to avoid this error.