Problem 59 Solve equation, and check your s... [FREE SOLUTION]

Chapter 2: Problem 59

Solve equation, and check your solution \(6 r-8 r=10\)

Short Answer

Expert verified

r = -5

Step by step solution

Combine Like Terms

First, combine the terms that contain the variable. In this case, combine the terms with 'r'. \[ 6r - 8r = 10 \] becomes \[ -2r = 10 \]

Isolate the Variable

Next, isolate the variable 'r' by dividing both sides of the equation by -2. \[ r = \frac{10}{-2} \] This simplifies to: \[ r = -5 \]

Check the Solution

Substitute the value of 'r' back into the original equation to verify the solution: \[ 6(-5) - 8(-5) = 10 \] Simplifies to: \[ -30 + 40 = 10 \] This holds true as 10 = 10.

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Key Concepts

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

Combining Like Terms

To solve an equation efficiently, it鈥檚 important to simplify it first. One key step in simplifying is combining like terms. Like terms are terms that contain the same variable raised to the same power. For example, in the equation given, you have two terms involving 'r':

Since these terms both contain 'r', you can combine them by performing the basic arithmetic operation between them. In this case, you perform subtraction:

6r - 8r = -2r. This results in a more straightforward equation:

\[ -2r = 10 \]
Combining like terms reduces the complexity of the equation and brings you one step closer to finding the solution.

Isolating the Variable

Once your equation is simplified, the next step is to isolate the variable. Isolating the variable means getting the variable by itself on one side of the equation. This helps you determine its exact value.

From the previous step, we have the equation:
\[ -2r = 10 \]
To isolate 'r', you need to perform the inverse operation of what's being done to 'r'. Here, 'r' is being multiplied by -2. The inverse operation is division.

Dividing both sides of the equation by -2, you get:
\[ r = \frac{10}{-2} \]This simplifies to:
\[ r = -5 \]At this stage, you now have the value of 'r'.

Checking the Solution

After solving for the variable, it's crucial to check your solution. This final step verifies that your solution is correct and that it satisfies the original equation.

Start by substituting the value of 'r' back into the original equation. In our case, the original equation was:
\[ 6r - 8r = 10 \]With the solved value, substitute -5 for 'r':
\[ 6(-5) - 8(-5) = 10 \]This simplifies to:
\[ -30 + 40 = 10 \]Since both sides of the equation are equal 鈥� 10 = 10 鈥� your solution is verified to be correct.
Checking the solution ensures that there are no mistakes in your algebraic manipulation and that your final answer is sound.

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91影视

Solve equation, and check your solution \(6 r-8 r=10\)

Short Answer

Step by step solution

Combine Like Terms

Isolate the Variable

Check the Solution

Key Concepts

Combining Like Terms

Isolating the Variable

Checking the Solution

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