Problem 11 Solve using the multiplication p... [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 11

Solve using the multiplication principle. Don't forget to check! $$ 7 x=-49 $$

Short Answer

Expert verified

x = -7

Step by step solution

Identify the equation

The given equation is \[ 7x = -49 \]

Apply the multiplication principle

To isolate the variable, divide both sides of the equation by 7. This gives\[ x = \frac{-49}{7} \]

Simplify the fraction

Simplify the fraction on the right-hand side:\[ x = -7 \]

Check the solution

Substitute $ x = -7 $ back into the original equation and verify:\[ 7(-7) = -49 \]Since both sides of the equation are equal, the solution is correct.

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Key Concepts

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

Multiplication Principle

The multiplication principle is a fundamental concept in algebra that helps in solving equations. When you have an equation like \[ 7x = -49 \], the principle allows you to multiply or divide both sides of the equation by the same non-zero number without changing the equality.

This means you can isolate the variable by performing the inverse operation. In our example, since 7 is multiplied by x, we will divide both sides by 7 to isolate x.

Isolating Variable

Isolating the variable means solving for the unknown, which in this case is x. To do this, we need to get x by itself on one side of the equation. In the given equation \[7x = -49\], our goal is to isolate x.

To achieve this, we use the multiplication principle and divide both sides by 7:

\[ x = \frac{-49}{7}\].

This isolation step is crucial because it directly shows the value of the unknown variable.

Simplify Fractions

Simplifying fractions makes the equation clearer and easier to work with. Once we have isolated the variable:

\[ x = \frac{-49}{7} \],

The next step is to simplify this fraction. Simplifying involves dividing the numerator by the denominator to get a whole number:

\[ \frac{-49}{7} = -7\].

So, we have \[ x = -7 \]. Always simplify fractions to their simplest form for clarity.

Check Solution

Checking your solution is essential to ensure it is correct. To do this, substitute the value you found for x back into the original equation. In this case, we substitute x = -7 back into \[ 7x = -49 \].

This gives us:

\[ 7(-7) = -49 \]

When we simplify the left side, it results in:

\[ -49 = -49 \]

Both sides are equal, confirming that our solution, x = -7, is indeed correct. Always remember to check your solution to avoid mistakes.

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91影视

Solve using the multiplication principle. Don't forget to check! $$ 7 x=-49 $$

Short Answer

Step by step solution

Identify the equation

Apply the multiplication principle

Simplify the fraction

Check the solution

Key Concepts

Multiplication Principle

Isolating Variable

Simplify Fractions

Check Solution

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