Problem 36 Evaluate each of the following e... [FREE SOLUTION]

91影视

Understanding Elementary Algebra with Geometry

Lewis Hirsch, Arthur Goodman

$Math Studyset 91影视 Explanations$ Math

6 Edition

Chapter 1: Problem 36

Evaluate each of the following expressions, if possible. $$7-3(5-9)$$

Short Answer

Expert verified

The value of the expression is $-5$.

Step by step solution

Simplify Inside the Parentheses

First, simplify the expression inside the parentheses: $5 - 9$. This results in $5 - 9 = -4$.

Multiply

Next, multiply the result from Step 1 by $-3$: $-3 \times -4$. This results in $-3 \times -4 = 12$.

Perform Addition and Subtraction

Finally, perform the subtraction: $7 - 12$. This results in $7 - 12 = -5$.

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Key Concepts

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

Order of Operations

In algebra, the order of operations is crucial for solving problems correctly. This order ensures that everyone gets the same result when evaluating mathematical expressions.
The common acronym to remember this sequence is PEMDAS:

P: Parentheses first
E: Exponents (i.e., powers and square roots, etc.)
M: Multiplication and D: Division (left to right)
A: Addition and S: Subtraction (left to right)

Let鈥檚 apply PEMDAS to the given problem:
Expression: $7 - 3(5 - 9)$.
According to PEMDAS, we first focus on simplifying the parentheses before performing any multiplication or subtraction.

Parentheses Simplification

Simplifying inside parentheses is our first step.
Inside the given expression, $7 - 3(5 - 9)$, we see the parentheses $(5 - 9)$.
Simplify it by performing the subtraction inside:

$5 - 9 = -4$

Now, our expression looks like this: $7 - 3(-4)$.
This step is vital because simplifying inside the parentheses first lays the groundwork for accurate further calculations, avoiding errors in the process.

Multiplication and Subtraction

With the parentheses simplified, we then address the remaining operations in the expression.
Our expression now is $7 - 3(-4)$.
According to the order of operations, we should handle the multiplication next:

Multiply $-3$ by $-4$: $-3 \times -4 = 12$

After multiplication, the expression simplifies to $7 - 12$.
Finally, we perform the subtraction:

$7 - 12 = -5$

Thus, the solution to the original expression $7 - 3(5 - 9)$ is $-5$.
Each step鈥攕implified parentheses, handled multiplication, and performed subtraction鈥攈elps ensure clarity and correctness in solving such problems.

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91影视

Evaluate each of the following expressions, if possible. $$7-3(5-9)$$

Short Answer

Step by step solution

Simplify Inside the Parentheses

Multiply

Perform Addition and Subtraction

Key Concepts

Order of Operations

Parentheses Simplification

Multiplication and Subtraction

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