Problem 7 Solve each equation. Check your ... [FREE SOLUTION]

Chapter 3: Problem 7

Solve each equation. Check your solution. $$-11=\frac{n}{-6}$$

Short Answer

Expert verified

The solution is $ n = 66 $.

Step by step solution

Eliminate the Fraction

To eliminate fractions in the equation \[ -11 = \frac{n}{-6} \]multiply both sides by $-6$, the denominator of the fraction:\[ -11 (-6) = \frac{n}{-6} (-6) \]which simplifies to:\[ 66 = n \]

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.

Solving equations

Equations are like balanced scales. Whatever you do to one side, you must do the same to the other side to keep the equation balanced. When solving an equation, the goal is to find out what value, when substituted for the variable, will make the equation true. Here, the equation is $-11 = \frac{n}{-6}$.We need to find the value of $n$ that makes both sides equal. Solving an equation typically involves a few steps:

Identify the operation involving the variable.
Perform inverse operations to isolate the variable.
Check your solution by substituting it back into the original equation.

Relying on the principle of keeping the equation balanced, the first step here involves removing the fraction, which we'll cover in the next section.

Fractions in equations

Fractions in equations can often make them a bit tricky. To simplify solving, we try to eliminate the fraction. In the equation $-11 = \frac{n}{-6}$, $-6$ is the denominator.To get rid of the fraction, multiply both sides by $-6$, which is the inverse operation of division:\[-11 (-6) = \frac{n}{-6} (-6)\]This action cancels out the fraction on the right side:\[66 = n\]The key here is remembering these two points:

Multiplying both sides by the denominator eliminates the fraction.
Whatever operation you perform must be done equally to both sides.

Dealing with fractions this way simplifies the problem, leaving you with a much easier equation to solve.

Basic algebra

Basic algebra is a method of solving mathematical puzzles using symbols, often letters, to represent unknown values. By learning a few rules and strategies, you can turn complex problems into straightforward solutions.In our example, the rule we focused on is that of inverse operations, which can simplify or unpack equations.

Understanding that multiplication and division are inverse operations helps break down equations.
Solving for a variable involves using these inverse operations to rearrange the equation.

In this context, we have unpacked the fraction using multiplication, resulting in $66 = n$. Here's another tip: As you build comfort with algebra, remember that practice helps recognize patterns and relations, leading to better problem-solving skills in math. Keep practicing these concepts, and soon solving equations will become like second nature!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Solve each equation. Check your solution. $$-11=\frac{n}{-6}$$

Short Answer

Step by step solution

Eliminate the Fraction

Key Concepts

Solving equations

Fractions in equations

Basic algebra

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Mechanics Maths

Pure Maths

Calculus

Decision Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.