Problem 88 - Algebra and Trigonometry

Question

Simplify each algebraic expression. $$2(5 x-1)+14 x$$

Step-by-Step Solution

Answer

The simplified expression of \(2(5x - 1) + 14x\) is \(24x - 2\).

Step 1: Apply the Distributive Property

The first step is to apply the distributive property. This means distributing the 2 to both \(5x\) and \(-1\). This results in \(2 \cdot 5x - 2 \cdot 1\). The property is applicable as follows: \(a(b + c) = ab + ac\).

Step 2: Perform the Multiplication

Perform the multiplication from the previous step. Thus, \(2 \cdot 5x - 2 \cdot 1\) becomes \(10x - 2\). After carrying out this multiplication, the expression now reads as \(10x - 2 + 14x\).

Step 3: Combine Like Terms

The final step is to combine like terms. In other words, add constants to constants and coefficients to coefficients. This simplifies \(10x - 2 + 14x\) to \(24x - 2\).