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The first step in solving a word problem involving an equation is setting up that equation. This means transforming the words into a mathematical statement. For our example, the problem says, 'What number added to 256 is 113?' We start by breaking down the problem. We know we are looking for a number which, when added to 256, gives us 113. Setting up the equation involves placing the unknown variable and the constants in the correct positions. In this case, we translate the sentence 'a number added to 256 is 113' into the equation: \( x + 256 = 113 \). The term 'x' is our placeholder for the unknown number. Using an equation setup, we organize the information in a format that allows us to solve for the unknown variable later.

In word problems, the unknown variable represents the value you need to find. We denote this unknown by a letter, commonly \( x \), but any letter can be used. In this exercise, 'What number added to 256 is 113?' the unknown number is the 'x'. By introducing an unknown, you create a standard form that allows you to manipulate and solve the problem. Using \( x \) helps you understand and follow through the necessary mathematical operations. So, whenever you come across a term you do not know, represent it with a variable.

Algebraic expressions are combinations of variables, numbers, and at least one arithmetic operation. In our equation, \( x + 256 = 113 \), \( x + 256 \) is the algebraic expression. This expression showcases the connection between the unknown variable \( x \) and the constant 256. Understanding how to form these expressions helps you translate words into numbers and operations. This translation is crucial in setting up the correct equations from word problems. Once set, the algebraic expression leads you towards solving the problem step by step.