Problem 51 - Introductory Algebra for College Students

Question

Simplify each algebraic expression. $$3+(x+11)$$

Step-by-Step Solution

Answer

The simplified form of the algebraic expression \(3 + (x + 11)\) is \(x + 14\).

Step 1: Identify the expression

The given algebraic expression is \(3 + (x + 11)\)

Step 2: Apply the applicable mathematical property

To simplify the expression, apply the associative property. This property states that the way in which numbers are grouped does not change their sum. In the expression \(3 + (x + 11)\), the brackets can be removed to re-write the expression as \(3 + x + 11\).

Step 3: Combine like terms

To further simplify the expression, combine the like terms. In the re-written expression \(3 + x + 11\), the like terms are 3 and 11 (the numeric constants). When summed, they yield \(x + 14\).