Problem 246 Solve each linear equation. $$... [FREE SOLUTION]

Chapter 2: Problem 246

Solve each linear equation. $$2(9 s-6)-62=16$$

Short Answer

Expert verified

s = 5

Step by step solution

Distribute the Constant

Multiply the constant outside the parentheses by each term inside the parentheses: 2(9s - 6) - 62 = 16 18s - 12 - 62 = 16

Combine Like Terms

Combine the constant terms on the left side of the equation: 18s - 74 = 16

Isolate the Variable Term

Add 74 to both sides of the equation to isolate the term with the variable: 18s - 74 + 74 = 16 + 74 18s = 90

Solve for the Variable

Divide both sides of the equation by 18 to solve for s: 18s / 18 = 90 / 18 s = 5

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Key Concepts

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

Distribution in Algebra

The first step when solving the equation $2(9s - 6) - 62 = 16$ is to distribute the constant outside the parentheses. Distribution means multiplying the constant by each term inside the parentheses. For our problem, we will multiply 2 by both 9s and -6. This will look like:

2(9s) + 2(-6) = 18s - 12

So, the equation now becomes: 18s - 12 - 62 = 16.

Remember, the distribution process helps transform the equation into a simpler form, making it easier to manage in subsequent steps.

Combining Like Terms

After distributing, the next step is combining like terms. In the equation 18s - 12 - 62 = 16, notice that -12 and -62 are both constant terms. We can combine these constants:

-12 - 62 = -74

This simplifies our equation to:

18s - 74 = 16

By combining like terms, we reduce the complexity of the equation, making it easier to isolate the variable.

Isolating Variables

To solve the equation 18s - 74 = 16, we need to isolate the variable term (18s) on one side of the equation. We can do this by adding 74 to both sides of the equation to cancel out the -74.

Here is how it works:

18s - 74 + 74 = 16 + 74

Now, the equation simplifies to:

18s = 90

Isolating the variable term ensures that we have the term with the variable by itself, which simplifies the solving process.

Solving for a Variable

Finally, we solve for the variable by simplifying the isolated variable term equation: 18s = 90. To find the value of s, we need to divide both sides of the equation by 18.

18s / 18 = 90 / 18

This gives us:

s = 5

Solving for a variable involves performing the necessary operations to find its exact value. In this case, by dividing both sides by 18, we determined that s equals 5. This means our solution to the original equation is s = 5.

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91影视

Solve each linear equation. $$2(9 s-6)-62=16$$

Short Answer

Step by step solution

Distribute the Constant

Combine Like Terms

Isolate the Variable Term

Solve for the Variable

Key Concepts

Distribution in Algebra

Combining Like Terms

Isolating Variables

Solving for a Variable

One App. One Place for Learning.

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