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Chapter 3: Problem 8

Evaluate the expression at the given value of \(\mathrm{x}\). $$-9 x+12\( at \)x=5$$

Short Answer

Expert verified
The result is -33.

Step by step solution

01

Substitute the Value of x

First, we need to substitute the given value of \( x \) into the expression. The expression is \(-9x + 12\), and we need to evaluate it when \( x = 5 \). So substitute 5 for \( x \) in the expression: \(-9(5) + 12\).
02

Multiply -9 and 5

Next, perform the multiplication for the term \(-9(5)\). Multiply \(-9\) by \(5\), which equals \(-45\). So now the expression becomes \(-45 + 12\).
03

Add -45 and 12

Finally, perform the addition of \(-45\) and \(12\). Compute \(-45 + 12\), which equals \(-33\). This is the evaluated result of the expression.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Substitution
Substitution is an essential step in evaluating expressions, especially when a specific value is provided for a variable. The idea is to replace each occurrence of the variable with the given numerical value. This allows you to transform a potentially abstract expression into one that can be calculated using basic arithmetic operations. For example, if you have the expression \(-9x + 12\) and are asked to evaluate it when \(x = 5\), you simply replace every instance of \(x\) with 5, resulting in \(-9(5) + 12\). This substitution prepares the expression for further evaluation.
Arithmetic Operations
Arithmetic operations are fundamental for simplifying expressions, once substitution has occurred. These operations include addition, subtraction, multiplication, and division. In our expression \(-9(5) + 12\), after substitution, we first conduct the multiplication \(-9 \times 5\), which equals \(-45\). Multiplication helps consolidate the expression into fewer terms, simplifying further calculations. Next, we apply addition by summing the resultant \(-45\) with 12, to achieve \(-33\). Each operation must follow its specific rules to ensure accurate results.
Order of Operations
The order of operations is a crucial set of rules that dictates the sequence in which mathematical operations are performed. This ensures consistency and accuracy in solving expressions. A common mnemonic to remember the order of operations is PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). In our expression \(-9(5) + 12\), the multiplication is handled before addition because multiplication takes precedence over addition. Ensuring operations are performed in the correct order prevents mistakes and produces the correct evaluated expression.

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