Problem 180 Solve the following equations wi... [FREE SOLUTION]

Chapter 2: Problem 180

Solve the following equations with constants on both sides. $$-62=8 n-6$$

Short Answer

Expert verified

n = -7.

Step by step solution

Isolate the variable term

Add 6 to both sides of the equation to move the constant term on the same side as the constant on the right-hand side. The equation becomes -62 + 6 = 8n - 6 + 6.

Simplify both sides

Simplify both sides of the equation: -56 = 8n.

Solve for the variable

Divide both sides by 8 to isolate n: -56 / 8 = 8n / 8, resulting in n = -7.

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Key Concepts

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

Isolate the Variable

When solving linear equations, the first step often involves isolating the variable. This means getting the variable term (like $8n$) on one side of the equation by itself.
In the exercise provided: $-62=8n-6$, we started by isolating the variable term by removing constants from the variable's side.
Since we had $-6$ on the same side as $8n$, we needed to eliminate it.
We added 6 to both sides of the equation, changing our equation to $-62 + 6 = 8n - 6 + 6$. This is because adding the same value to both sides of an equation keeps the equation balanced.
After simplifying, we have $-56 = 8n$.
Now, the variable term is isolated, making it easier to solve for $n$.

Simplify the Equation

Simplifying the equation means making it easier to understand and solve by combining like terms and clearing out unnecessary parts.
After isolating the variable in our example, we got $-56 = 8n$.
Both sides are now simplified into the most basic forms.
Simplifying the equation helps us see the relationship between the terms more clearly, and it sets up the final step for solving.
For example, if the left side had more complex terms, we would combine them or simplify them before moving on.
The idea is to make the equation as straightforward as possible before solving it.

Constants on Both Sides

In linear equations, you often encounter constants on both sides. Managing them effectively is crucial for solving the equation.
In our example, we encountered the constant $-6$ on the same side as our variable term $8n$.
To manage this, we moved the $-6$ by adding 6 to both sides: $-62 + 6 = 8n - 6 + 6$.
This step simplifies the equation by bringing constants together while keeping it balanced.
The final form before solving is $-56 = 8n$, with all constants being managed on one side, making it easier to isolate and solve for the variable.

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91影视

Solve the following equations with constants on both sides. $$-62=8 n-6$$

Short Answer

Step by step solution

Isolate the variable term

Simplify both sides

Solve for the variable

Key Concepts

Isolate the Variable

Simplify the Equation

Constants on Both Sides

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