Problem 72 Solve and check. $$6 a+3+2 a=11$... [FREE SOLUTION]

Chapter 5: Problem 72

Solve and check. $$6 a+3+2 a=11$$

Short Answer

Expert verified

The solution to the equation is $a = 1$.

Step by step solution

Combine Like Terms

Identify like terms and combine them. In this equation, the like terms are $6a$ and $2a$. Combining them, we have $8a + 3 = 11$.

Solve Equation

Next, isolate the variable 'a'. Subtract 3 from both sides of the equation to get $8a = 8$. Afterwards, divide both sides by 8 to solve for 'a'. This gives $a = 1$.

Check Solution

Finally, substitute the value of 'a' back into the original equation to check the solution. That gives us $6(1) + 3 + 2(1) = 11$. If the solution is correct, both sides of the equation must balance. Evaluating the left side gives $6 + 3 + 2 = 11$, which proves our solution is correct.

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Key Concepts

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

Understanding Like Terms

In any linear equation, recognizing and combining like terms is a fundamental step. Like terms are terms that contain the same variable raised to the same power. In our exercise, the terms $6a$ and $2a$ are like terms because they both contain the variable $a$. When combining like terms, simply add or subtract the coefficients (the numbers in front of the variables).For example:

Combine $6a$ and $2a$ to get $8a$.

This simplifies the equation, making it easier to solve. By combining like terms, you're effectively consolidating information to reduce clutter in your equation, which is especially helpful before moving on to isolating the variable.

Isolating the Variable

Once you have simplified the equation by combining like terms, the next step is isolating the variable. This means we need 'a' on one side of the equation by itself. In the equation $8a + 3 = 11$, start by removing the constant term from the side of the equation with the variable.Here's how it works:

Subtract 3 from both sides to align the equation, resulting in $8a = 8$.
Then, divide both sides by 8 so that 'a' is isolated, giving us $a = 1$.

These operations ensure that the equation remains balanced while you solve for the variable, which is the primary goal in solving linear equations. Isolating the variable is crucial for finding the numerical solution to the equation.

Checking Solutions

After finding a solution, it's important to verify its correctness by substituting the solution back into the original equation. If the left and right sides of the equation are equal, your solution is accurate.To check the solution for $a = 1$:

Substitute $1$ for 'a' in the original equation: $6(1) + 3 + 2(1)$.
Simplify the expression to see if it equals 11.
Calculate: $6 + 3 + 2 = 11$.

Both sides equal 11, confirming that $a = 1$ is indeed the correct solution. Checking solutions is a critical final step because it ensures the accuracy of your work and confirms that you haven't made any missteps along the way.

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91影视

Solve and check. $$6 a+3+2 a=11$$

Short Answer

Step by step solution

Combine Like Terms

Solve Equation

Check Solution

Key Concepts

Understanding Like Terms

Isolating the Variable

Checking Solutions

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