In Exercises 121–128, write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. Eight decreased by three times the sum of a number and six

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Start by carefully translating the English phrase into an algebraic expression. The phrase 'Eight decreased by' means we are subtracting something from 8.

Next, identify what is being subtracted. The phrase 'three times the sum of a number and six' indicates that we need to multiply 3 by the sum of a number (represented by x) and 6.

Write the sum of the number and six as (x + 6). Then, multiply this sum by 3 to get 3(x + 6).

Now, subtract this entire expression, 3(x + 6), from 8. This gives the algebraic expression: 8 - 3(x + 6).

Simplify the expression by distributing the -3 across the terms inside the parentheses: 8 - 3x - 18. Combine like terms to simplify further: -3x - 10.

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Algebraic Expressions

An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols. It represents a value and can be simplified or manipulated according to algebraic rules. Understanding how to translate verbal phrases into algebraic expressions is crucial for solving problems in algebra.

Order of Operations

The order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed to ensure consistent results. The common acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. Applying these rules correctly is essential when simplifying algebraic expressions.

Combining Like Terms

Combining like terms is the process of simplifying an algebraic expression by adding or subtracting terms that have the same variable raised to the same power. This step is important for reducing expressions to their simplest form, making it easier to solve equations or evaluate expressions.