Problem 44 Solve using the addition princip... [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 44

Solve using the addition principle. $$ -7.8=2.8+x $$

Short Answer

Expert verified

x = -10.6

Step by step solution

Identify the equation

The given equation is \[ -7.8 = 2.8 + x \].

Isolate the variable term

To isolate the variable term $x$, subtract 2.8 from both sides of the equation \[ -7.8 - 2.8 = 2.8 + x - 2.8 \].

Simplify both sides

Simplify the equation to find $x$. The left side simplifies to \[ -10.6 \]. The right side simplifies to \[ x \]. Therefore, the equation becomes \[ -10.6 = x \].

Conclusion

We have determined that \[ x = -10.6 \] by isolating the variable and simplifying both sides.

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Key Concepts

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

solving equations

Solving equations is a fundamental skill in algebra. An equation is like a balanced scale鈥攚hatever we do to one side, we must do to the other to keep it balanced. There are several methods for solving equations, but one common method is using the addition principle. This method involves isolating the variable (the unknown you're solving for) on one side of the equation. Understanding how to maintain equality while manipulating both sides is crucial in solving equations efficiently.

isolating variables

To isolate variables means to get the unknown (variable) by itself on one side of the equation. Let's use an example to illustrate:

The equation is \[ -7.8 = 2.8 + x \].

Here, we need to isolate $x$ from the rest. To do this, we look at what is added or subtracted to $x$ and do the opposite operation to both sides of the equation. In this case, $2.8$ is added to $x$, so we subtract $2.8$ from both sides:

\[ -7.8 - 2.8 = 2.8 + x - 2.8 \]

This way, $x$ is isolated. The main goal is to perform the same mathematical operation on both sides to keep the equation balanced, which will help to isolate the variable.

simplifying equations

Simplifying equations is key to making them easier to solve. Once we've performed operations to both sides, we need to ensure everything is as simple as possible. Let's break down the simplification process from our example:

Original equation: \[ -7.8 = 2.8 + x \].

After subtracting $2.8$ from both sides, we simplify:

\[ -7.8 - 2.8 = x \]

Combining like terms on the left side gives:\[ -10.6 = x \]

Simplification often involves combining like terms (numbers without variables) and ensuring the variable is isolated and easy to read. Finally, never forget to check your work by substituting the solution back into the original equation to confirm it balances both sides.

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91影视

Solve using the addition principle. $$ -7.8=2.8+x $$

Short Answer

Step by step solution

Identify the equation

Isolate the variable term

Simplify both sides

Conclusion

Key Concepts

solving equations

isolating variables

simplifying equations

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