/*! 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 13 Solve each equation using the Su... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 13

Solve each equation using the Subtraction and Addition Properties of Equality. $$a-45=76$$

Short Answer

Expert verified
\( a = 121 \)

Step by step solution

01

Understand the Equation

The given equation is \( a - 45 = 76 \). The goal is to isolate the variable \( a \) on one side of the equation.
02

Add 45 to Both Sides

Use the Addition Property of Equality to add 45 to both sides of the equation to cancel out the -45. The equation now looks like this: \[ a - 45 + 45 = 76 + 45 \]
03

Simplify Both Sides

Simplify the left side and the right side of the equation. On the left side, -45 and 45 cancel each other out, leaving just \( a \). On the right side, add 76 and 45: \[ a = 121 \]

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.

solving linear equations
When you are solving linear equations, your goal is to find the value of the variable that makes the equation true.
In this case, the variable is represented by the letter 'a'. For example, in the equation given, you need to solve for 鈥榓鈥�:
This process involves combining like terms and isolating the variable on one side of the equation. This makes it easier to see what value the variable must have to satisfy the equation.
By following certain steps systematically, we can find the correct solution.
isolate the variable
To isolate the variable means to get the variable by itself on one side of the equation.
This is a crucial step because once you isolate the variable, you can easily find its value.
Using the given equation, let's look at the steps:

  • Start with the equation: \( a - 45 = 76 \)

  • The goal is to have 'a' by itself on one side, so we need to eliminate the -45.
  • To do this, we use the Addition Property of Equality and add 45 to both sides of the equation:
    \( a - 45 + 45 = 76 + 45 \)

This will cancel out the -45 on the left side of the equation:
\( a = 121 \)
Now, 'a' is isolated and we know its value.
simplifying equations
Simplifying equations means making them easier to read and solve.
This often involves combining like terms, removing coefficients by division, or cancelling out terms using addition or subtraction.
Let's break down how we simplified our equation:

  • We started with: \( a - 45 + 45 = 76 + 45 \)

  • On the left side, the -45 and +45 cancel out, leaving us with: \( a \)

  • On the right side, we can simply add the numbers together: \( 76 + 45 = 121 \)


Simplifying makes it clear that: \( a = 121 \)

By following these steps, you can tackle more complex equations using the same principles.

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

Solve each inequality, graph the solution on the number line, and write the solution in interval notation. $$\frac{n}{13} \leq-6$$

Solve each inequality, graph the solution on the number line, and write the solution in interval notation. $$9 p>14 p-18$$

Graph each inequality on the number line and write in interval notation. (a) \(x>3\) (b) \(x \leq-0.5\) (c) \(x \geq \frac{1}{3}\)

Solve each inequality, graph the solution on the number line, and write the solution in interval notation. $$\frac{3}{5} x \leq-45$$

Translate and solve. Then write the solution in interval notation and graph on the number line. Ten times \(y\) is at most -110 .
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Decision 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.