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Chapter 1: Problem 69

Simplify each expression. \(-6-4(y-7)\)

Short Answer

Expert verified
The simplified expression is 22 - 4y.

Step by step solution

01

Distribute the negative sign

Distribute the -4 to both terms inside the parentheses: -6 - 4(y - 7) = -6 - 4y + 28.
02

Combine like terms

Combine the constant terms -6 and +28: -6 + 28 = 22. The simplified expression is 22 - 4y.

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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 is a key concept in algebra. It allows you to multiply a single term by multiple terms inside parentheses. In the exercise, we started with the expression \(-6 - 4(y - 7)\). To simplify, we distribute \(-4\) to both \(y\) and \(-7\):
\-4 * y = -4y
-4 * -7 = 28
So the expression becomes \(-6 - 4y + 28\). Distributing helps break down complex expressions, making them easier to handle.
Combining Like Terms
Combining like terms is an essential process in algebraic simplification. In our expression \(-6 - 4y + 28\), we can only combine the constant terms \(-6\) and \(28\) since they do not have any variables attached. Adding these constants together:
-6 + 28 = 22
This updates our simplified expression to \(22 - 4y\). Remember, like terms are terms with the same variables raised to the same power. Combining these helps simplify your equations and inequalities.
Algebraic Simplification
Algebraic simplification is a step-by-step approach to make expressions easier to work with. By following the steps of distribution and combining like terms, we transformed the expression \(-6 - 4(y - 7)\)into a simpler form \(22 - 4y\). Simplification often involves:
1. Using the distributive property
2. Combining like terms
3. Removing parentheses
This reduces the complexity of solving or studying the expressions. Simplified expressions are more manageable and make further calculations easier.

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Most popular questions from this chapter

Write each sentence as an equation, using \(x\) as the variable. Then find the solution of the equation from the set of integers between -12 and \(12,\) inclusive. An integer is divisible by 4 if its last two digits form a number divisible by \(4,\) and not otherwise. (a) Is 2,876,335 divisible by \(4 ?\) (b) Is 6,221,464 divisible by \(4 ?\)

Write a numerical expression for each phrase, and simplify the expression. The sum of -7 and -13 , increased by 14

Write each expression without parentheses. $$ -(-z+5 w-9 y) $$

Write each sentence as an equation, using \(x\) as the variable. Then find the solution of the equation from the set of integers between -12 and \(12,\) inclusive. An integer is divisible by 9 if the sum of its digits is divisible by \(9,\) and not otherwise. (a) Is 2,287,321 divisible by \(9 ?\) (b) Is 4,114,107 divisible by \(9 ?\)

Use the distributive property to rewrite each expression. $$ 5(w+4) $$
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