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The distributive property is a fundamental concept in algebra that helps us simplify expressions by removing parentheses. It is expressed as multiplying each term inside a grouping, like parentheses, by another term outside of it. In our given problem, we have the expression:\[11x + 3(8-x)\]To solve this, we apply the distributive property by distributing the multiplier 3 across the terms within the parentheses. This means:- Multiply 3 by 8, to get 24.- Multiply 3 by \(-x\), which gives \(-3x\).So, the expression becomes:\[11x + 24 - 3x\]By using the distributive property, we effectively eliminate the parentheses and transform the expression into a simpler form that's easier to work with.

After using the distributive property, the next step in simplifying an expression is combining like terms. Like terms are terms that have the same variable raised to the same power. They can be combined through addition or subtraction to further simplify the expression.In the expression we derived:\[11x + 24 - 3x\]- Notice the terms with \(x\): \(11x\) and \(-3x\).- They are like terms because they have the same variable, \(x\).- Combine them: \(11x - 3x = 8x\).This leaves us with the simplified expression:\[8x + 24\]By combining like terms, we consolidate the expression into fewer terms, which simplifies the calculation and makes it easier to understand.

An algebraic expression is a mathematical phrase that includes numbers, variables, and operation symbols. It does not include an "equals" sign, so it's not an equation but a statement showing a value.The initial expression given:\[11x + 3(8-x)\]Is an algebraic expression because:- It contains numbers 11, 3, and 8.- It includes a variable, \(x\), which represents an unknown value.- It involves operations like addition and multiplication.In algebra, expressions like these are manipulated using properties like the distributive property and combining like terms to simplify or evaluate for specific values of the variables. Simplifying expressions makes it easier to solve problems and is an essential skill in algebra and other areas of mathematics. Understanding how to navigate through these components in an expression allows for effective problem-solving and mathematical reasoning.