Problem 28 Solve. $$ 6.8 y-2.4 y=-88 ... [FREE SOLUTION]

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Basic College Mathematics

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

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 11: Problem 28

Solve. $$ 6.8 y-2.4 y=-88 $$

Short Answer

Expert verified

y = -20

Step by step solution

Combine Like Terms

Combine the terms with the variable y. The equation is given by: \[ 6.8y - 2.4y = -88 \]. Subtract 2.4y from 6.8y to get: \[ 4.4y = -88 \].

Solve for y

Divide both sides of the equation by 4.4 to isolate the variable y: \[ y = \frac{-88}{4.4} \].

Simplify the Solution

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 in Linear Equations

When you solve linear equations, one of the most important steps is combining like terms. This means we need to simplify the equation by putting together terms that have the same variable. For example, in the equation given: $ 6.8y - 2.4y = -88 $, both $ 6.8y $ and $ 2.4y $ contain the variable y. To combine these, you subtract $ 2.4y $ from $ 6.8y $, which results in: \: \[ 4.4y = -88 \]. This step makes the equation simpler, enabling us to solve it more easily.

Combining like terms is key because it reduces the complexity and number of terms in the equation. This makes the subsequent steps much more manageable.

Isolating Variables in Linear Equations

After combining like terms, the next crucial step is isolating the variable. To isolate a variable means to get the variable alone on one side of the equation. This often involves operations like addition, subtraction, multiplication, or division. In our example: \[ 4.4y = -88 \], we need to solve for y. To do this, we want to isolate y by getting rid of the coefficient 4.4.
To isolate y, we divide both sides of the equation by 4.4: \[ y = \frac{-88}{4.4} \].

When isolating variables, remember the golden rule of equations: whatever you do to one side, you must do to the other. This maintains the balance of the equation.

Division in Algebra

The final step in solving many linear equations often involves division. Division is used to simplify the coefficient of the variable to 1. Let's take our example, where we have already simplified and isolated: \[ y = \frac{-88}{4.4} \].

Here, $ 4.4 $ is the coefficient of y, which we divide into $ -88 $. Doing the math, we get: \[ y = -20 \].

Division in algebra is important because it helps break down expressions into simpler forms, making solving for the variable straightforward. Just remember, division should be done as the last step after combining like terms and isolating the variable.

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91影视

Solve. $$ 6.8 y-2.4 y=-88 $$

Short Answer

Step by step solution

Combine Like Terms

Solve for y

Simplify the Solution

Key Concepts

Combining Like Terms in Linear Equations

Isolating Variables in Linear Equations

Division in Algebra

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