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Chapter 1: Problem 78

Simplify each expression. $$ -5(8 x+2)-(5 x-3)-3 x+17 $$

Short Answer

Expert verified
-48x + 10

Step by step solution

01

Distribute the -5

Multiply each term inside the parentheses by -5: -5(8x) - 5(2) = -40x - 10
02

Distribute the negative sign

Distribute the negative sign through the second parentheses: -(5x - 3) = -5x + 3
03

Combine like terms

Combine all like terms: -40x - 10 - 5x + 3 - 3x + 17
04

Simplify the expression

Add up all the x terms and constant terms: -40x - 5x - 3x = -48x -10 + 3 + 17 = 10 The simplified expression is: -48x + 10

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Key Concepts

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

distributive property
The distributive property allows us to simplify expressions by removing parentheses. When you have a term outside the parentheses, you multiply it by each term inside the parentheses. For example, in the expression -5(8x + 2), multiply -5 by both 8x and 2.
This results in -40x - 10.
Remember, the distributive property helps break down more complex expressions into simpler parts that we can then easily handle.
combining like terms
After using the distributive property, the next step is combining like terms. Like terms are terms that have the same variable raised to the same power. For instance, consider the expression: \(-40x - 10 - 5x + 3 - 3x + 17\).
Here, we have three groups of terms:
  • Like terms with 鈥榵鈥�:-40x, -5x, -3x
  • Constants: -10, 3, 17
Combine the 鈥榵鈥� terms: -40x - 5x - 3x = -48x
Then, combine the constants: -10 + 3 + 17 = 10
This will further simplify your expression.
constants in algebra
Constants are numbers without variables. They simply stand alone. In the given expression -5(8x + 2) - (5x - 3) - 3x + 17, constants are numbers like 2, -3, -10, 3, and 17.
When simplifying, combine these constants to reduce the expression further.
For instance, combining -10, 3, and 17 gives us: -10 + 3 + 17 = 10.
Simplifying constants helps to narrow down the expression to its final form, making calculations easier and more manageable.

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