Problem 87 - Algebra and Trigonometry

Question

Simplify each algebraic expression. $$5(3 x-2)+12 x$$

Step-by-Step Solution

Answer

After simplifying the expression \(5(3 x-2)+12 x\), you get \(27x -10\).

Step 1: Apply the Distributive Property

First off, apply the distributive property to the expression \(5(3 x-2)+12 x\). According to the distributive property, you can multiply the number outside the parentheses, which is 5 in this case, with each term inside the parentheses, i.e., \(3x\) and \(-2\). Doing this gives \(5*3x - 5*2 + 12x\) which simplifies to \(15x -10 + 12x\).

Step 2: Combine Like terms

After applying the distributive property, the expression has become \(15x -10 + 12x\). Now you can combine the like terms, which in this case are \(15x\) and \(12x\). Adding these together leads to the simplified expression: \(27x -10\).