Problem 197 Solve the following equations wi... [FREE SOLUTION]

Chapter 2: Problem 197

Solve the following equations with variables on both sides. $$-11 r-8=-7 r$$

Short Answer

Expert verified

r = -2

Step by step solution

Move the variable terms to one side

To start, add $11r$ to both sides of the equation to move all the variable terms to one side.dash7r = -8dash + 11rdash -11r - 8 = -7rdash = just write-8 + 11rThis simplifies to:-8 = 4r

Isolate the variable

Now, divide both sides of the equation by 4 to solve for r.dash8/4 + 11r/4 +2 r

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Key Concepts

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

Equations with Variables on Both Sides

When solving equations with variables on both sides, it's crucial to get all the variable terms on one side and constants on the other. This process often involves adding or subtracting terms from both sides of the equation. For instance, in the equation $$-11r - 8 = -7r$$, we have variables (r) on both sides.

The goal here is to combine like terms, which are the terms involving variables, so that you have all of them on one side. This usually makes it easier to simplify and solve the equation.

Let's look at the provided example for clarity.

Isolating the Variable

Once the variable terms are on one side of the equation, the next step is to isolate the variable. This often involves moving constant terms to the other side of the equation and simplifying.

For the given equation $$-11r - 8 = -7r$$, the first step is to move the variable terms to one side:
Add $$11r$$ to both sides:
$$-11r - 8 + 11r = -7r + 11r$$
This simplifies to: $$-8 = 4r$$

Now, to isolate the variable (r), divide both sides by 4:
\frac{-8}{4} = \frac{4r}{4}$$
which simplifies to:$$r = -2$$.
This gives us our solution.

Isolating the variable is a critical step in solving algebraic equations, making it easier to find the value of the unknown variable.

Simplifying Algebraic Expressions

Simplifying algebraic expressions is a fundamental skill in algebra. It involves combining like terms, reducing fractions, and re-writing expressions in a simpler form.

In the given example, after bringing all variable terms to one side and constants to the other, you simplified from:$$-11r - 8 = -7r$$ to:$$-8 = 4r$$.
This simplification made it possible to easily isolate the variable (r).

Simplifying helps in reducing complexity and making equations more manageable. Always look to combine like terms and perform any possible arithmetic to simplify the equation before finalizing your solution.

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91影视

Solve the following equations with variables on both sides. $$-11 r-8=-7 r$$

Short Answer

Step by step solution

Move the variable terms to one side

Isolate the variable

Key Concepts

Equations with Variables on Both Sides

Isolating the Variable

Simplifying Algebraic Expressions

One App. One Place for Learning.

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