/*! 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 11 Solve the equations. $$y+8.4=9... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 11

Solve the equations. $$y+8.4=9.26$$

Short Answer

Expert verified
y = 0.86

Step by step solution

01

Write Down the Equation

Start with the given equation: y + 8.4 = 9.26
02

Isolate the Variable y

To isolate y, subtract 8.4 from both sides of the equation: y = 9.26 - 8.4
03

Perform the Subtraction

Now, perform the subtraction to find the value of y: y = 0.86

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.

Isolate the Variable
When solving linear equations, one of the essential steps is to isolate the variable. This means you want to get the variable (like y) on one side of the equation by itself.
Think of it as separating the variable from the rest of the terms to find out its value.
To isolate the variable, you typically use addition, subtraction, multiplication, or division, depending on how the equation is set up.
In the example equation, $$y + 8.4 = 9.26$$, you can isolate y by performing an inverse operation.
Here, you see that 8.4 is added to y.
The opposite of addition is subtraction, so you'll subtract 8.4 from both sides to isolate y.
Subtraction
Subtraction is a fundamental operation in algebra and is crucial when isolating variables.
To subtract means to take one quantity away from another.
When isolating a variable, you often subtract a number from both sides of an equation to keep it balanced.
Applying this to our example, we see:
  • Start with the equation: \(y + 8.4 = 9.26\).
  • Subtract 8.4 from both sides: \(y = 9.26 - 8.4\).
Now, perform the subtraction:
\(9.26 - 8.4 = 0.86\).
This leaves you with \(y = 0.86\).
Remember, always do the same operation on both sides of the equation to maintain balance.
Basic Algebra
Algebra forms the foundation for understanding other areas of mathematics and science.
Linear equations like the one we solved are some of the basic building blocks.
An equation states that two expressions are equal.
To solve for a variable means to find the value that makes this statement true.
In the example equation \(y + 8.4 = 9.26\), you mix several core algebra concepts:
  • Understanding equality: knowing both sides of the equation represent the same value.
  • Performing operations: using subtraction to isolate the variable.
  • Solving: finding that \(y = 0.86\) satisfies the equation.
Mastering these basic algebra skills is essential for tackling more complex problems in math and science.

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

Round the number to the indicated place value. $$\begin{array}{|l|l|l|l|l|l|} \hline & \text { Number } & \text { Hundreds } & \text { Tens } & \text { Tenths } & \text { Hundredths } & \text { Thousandths } \\ \hline& 971.0948 & & & & & \\ \hline & {} & & & & & \\ \hline & {} & & & & & \\ \hline \end{array}$$

A hotel gift shop ordered 40 T-shirts at \(\$ 8.69\) each, 10 hats at \(\$ 3.95\) each, and 20 beach towels at \(\$ 4.99\) each. What was the total cost of the merchandise, including the \(\$ 29.21\) sales \(\operatorname{tax} ?\)

When multiplying or dividing decimals, it is important to place the decimal point correctly. Determine whether you think the number is reasonable or unreasonable. If the number is unreasonable, move the decimal point to a position that makes more sense. Mickey makes \(8.50 per hour. He estimates his weekly paycheck to be \)3400.

The exercise wheel for Al's dwarf hamster has a diameter of 6.75 in. a. Find the circumference. Use 3.14 for \(\pi\) and round to the nearest inch. b. How far does Al's hamster travel if he completes 25 revolutions? Write the answer in feet and round to the nearest foot.

Divide. Round the answer to the indicated place value. Use the rounded quotient to check. $$4.96 \div 0.24 \text { thousandths }$$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

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.