Problem 27 Solve. $$ 10.2 y-7.3 y=-58 ... [FREE SOLUTION]

91影视

Basic College Mathematics

Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 11: Problem 27

Solve. $$ 10.2 y-7.3 y=-58 $$

Short Answer

Expert verified

y = -20

Step by step solution

Combine Like Terms

First, combine the terms involving the variable on the left side of the equation. $10.2y - 7.3y = -58$Combine the coefficients of the variable: $2.9y = -58$

Isolate the Variable

Next, isolate the variable by dividing both sides of the equation by the coefficient of the variable, which is 2.9. $y = \frac{-58}{2.9}$

Simplify the Equation

Perform the division to find the value of $y$. $y = -20$

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Key Concepts

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

combining like terms

Combining like terms is one of the fundamental steps in solving linear equations. It refers to the process of adding or subtracting terms that have the same variable component. For instance, in the exercise given, both terms 10.2y and 7.3y have the variable 'y'. Thus, they are called like terms. To combine them, simply add or subtract their coefficients. In our case, this meant performing the operation 10.2 - 7.3, which results in 2.9. So the equation transforms from 10.2y - 7.3y = -58 to 2.9y = -58. This step simplifies the equation significantly and reduces the complexity, making it easier to manage.

isolating variables

Isolating the variable is the process of getting the variable by itself on one side of the equation. After combining like terms, you want to solve for y but it鈥檚 currently multiplied by 2.9. To do this, you'll have to eliminate the 2.9 that is attached to y. This is done by dividing both sides of the equation by 2.9鈥攅ffectively 'isolating' y.

So we take 2.9y = -58 and divide each side by 2.9: \[y = \frac{-58}{2.9}\]

This operation moves us closer to finding the actual value of y. Once the variable is isolated, you can easily simplify to find its value.

arithmetic operations

Arithmetic operations include addition, subtraction, multiplication, and division. These operations are tools we use to manipulate equations to solve for a variable. In isolating the variable y, you will use division. In the specific exercise, after isolating y, the equation was: \[y = \frac{-58}{2.9}\]

By performing the division operation on the right-hand side, we simplify the equation: \[y = -20\]

In this way, arithmetic operations help refine our equation step by step鈥攆rom combining like terms, isolating the variable, to simplifying and finding the answer. Each arithmetic operation relates back to making the equation more manageable and ultimately, solvable.

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91影视

Solve. $$ 10.2 y-7.3 y=-58 $$

Short Answer

Step by step solution

Combine Like Terms

Isolate the Variable

Simplify the Equation

Key Concepts

combining like terms

isolating variables

arithmetic operations

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