/*! 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 66 Simplify each expression. $$ ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 66

Simplify each expression. $$ -4-5(t-13) $$

Short Answer

Expert verified
Simplified expression: 61 - 5t.

Step by step solution

01

Distribute the -5

To simplify the expression -4-5(t-13), first distribute the -5 inside the parentheses. This means multiplying -5 by every term inside the parentheses: -4 - 5(t - 13) = -4 - 5t + 65.
02

Combine like terms

Now, combine the constant terms -4 and +65. Performing the addition: -4 + 65 = 61. So the simplified expression is 61 - 5t.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Distributive Property
When simplifying algebraic expressions, the distributive property is a powerful tool. It helps to eliminate parentheses by distributing (multiplying) a number outside the parentheses by each term inside. In our exercise, we distributed -5 across each term within the parentheses (t - 13).
This means:
-5 * t = -5t
-5 * (-13) = +65
So, -4 - 5(t - 13) becomes -4 - 5t + 65. Mastering this property is essential for simplifying expressions accurately.
Combining Like Terms
Combining like terms means adding or subtracting terms that have the same variable part. After using the distributive property, you often have to combine these terms to simplify the expression further. In our example, the terms -4 and +65 are constants (they do not have variables).
By combining them:
-4 + 65 = 61.
The expression now reads 61 - 5t. Always look for terms with the same variable or the same constant value for combining.
Linear Expressions
Linear expressions are algebraic expressions where the variable(s) are to the first power, and no variables are multiplied or divided by each other. In other words, the highest exponent of the variable in a linear expression is one. For example, 61 - 5t is a linear expression because the variable t is not squared, cubed, or in higher exponents. Linear expressions are straightforward to work with, as the simplification process involves distributing, combining like terms, and arranging them neatly. Understanding linear expressions prepares you for more complex algebraic operations later on.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Simplify each expression. $$ -\frac{4}{3}(y-12)-\frac{1}{6} y $$

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) $$ \left(\frac{5}{6} x+\frac{3}{2} y\right)\left(-\frac{1}{3} a\right) $$

A pilot announces to the passengers that the current altitude of their plane is \(34,000\) ft. Because of turbulence, the pilot is forced to descend \(2100 \mathrm{ft}\). Write the new altitude as a signed number.

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

Translate each phrase into a mathematical expression. Use \(x\) as the variable. Combine like terms when possible. Six times a number, added to the sum of the number and six
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.