Problem 91 - Algebra and Trigonometry

Question

Simplify each algebraic expression. $$5(3 y-2)-(7 y+2)$$

Step-by-Step Solution

Answer

The simplified algebraic equation is \( 8y - 12 \)

Step 1: Apply the Distributive Law

The Distributive Law, also known as the distributive property, allows us to remove parentheses by multiplying a single term on the outside of a set of parentheses by every term inside. Apply the distributive law to remove the parentheses: \(5 \times 3y - 5 \times 2 - 7y - 2\).

Step 2: Multiply through

Next, multiply through to achieve: \(15y - 10 - 7y - 2\)

Step 3: Combine Like Terms

Lastly, combine the 'y' terms together and the number terms together. The result is: \( (15y - 7y) - (10 + 2)\)