/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 289 Simplify each expression. $$ ... [FREE SOLUTION] | 91影视

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Chapter 1: Problem 289

Simplify each expression. $$ 26-3(2-7) $$

Short Answer

Expert verified
11

Step by step solution

01

Simplify Inside the Parentheses

First, simplify the expression inside the parentheses: 2 - 7 = -5.
02

Multiply by the Number Outside the Parentheses

Next, multiply the result by -3: -3(-5) = 15.
03

Subtract from the Original Number

Finally, subtract the product from the original number: 26 - 15 = 11.

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Key Concepts

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

Order of Operations
Understanding the order of operations is crucial in algebra simplification. The order of operations dictates the sequence in which the different operations (+, -, *, /, etc.) must be performed to ensure a consistent result. The acronym PEMDAS can help you remember this order:

  • P 鈥� Parentheses
  • E 鈥� Exponents
  • M 鈥� Multiplication
  • D 鈥� Division
  • A 鈥� Addition
  • S 鈥� Subtraction

This means that any calculation inside parentheses needs to be handled first. Then, we deal with exponents, followed by multiplication and division from left to right. Finally, addition and subtraction are performed from left to right. In the exercise provided, the expression to simplify is 26 - 3(2 - 7). According to the order of operations, we start with the parentheses: (2 - 7).
Parentheses in Algebra
Parentheses play a crucial role in algebra as they indicate which operations should be performed first. In our exercise, the expression 26 - 3(2 - 7) contains parentheses. According to the order of operations (PEMDAS), we need to simplify what鈥檚 inside the parentheses before dealing with other operations.

So, for the expression 2 - 7:
  • 2 鈥� 7 equals -5.

Now that we have simplified what鈥檚 inside the parentheses, we can proceed to the multiplication step:
The modified expression is now 26 - 3(-5).
Simplifying Expressions
After simplifying inside the parentheses and dealing with multiplication, we need to simplify the entire expression further. For our exercise, once we have 26 - 3(-5), we need to multiply -3 by -5.
  • -3 * -5 equals 15 (Remember, multiplying two negative numbers results in a positive number).

Next, we perform the final subtraction: 26 - 15, which equals 11. Simplifying expressions involves combining like terms, reducing fractions, and performing operations in the correct order.
This ensures that the expression is fully simplified, making it easier to understand and use in further calculations.

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