Solve For $x$ In The Equation $a X + 7 = 12$.A. $5 - A$ B. $\frac{5}{a}$ C. $\frac{19}{a}$ D. $19 + A$

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Understanding the Equation

The given equation is $a x + 7 = 12$. To solve for $x$, we need to isolate the variable $x$ on one side of the equation. This involves performing algebraic operations to simplify the equation and make it easier to solve.

Isolating the Variable

To isolate $x$, we need to get rid of the constant term $7$ on the left-hand side of the equation. We can do this by subtracting $7$ from both sides of the equation. This gives us:

$a x + 7 - 7 = 12 - 7$

Simplifying the equation, we get:

$a x = 5$

Solving for $x$

Now that we have isolated $x$, we can solve for its value. To do this, we need to get rid of the coefficient $a$ that is being multiplied by $x$. We can do this by dividing both sides of the equation by $a$. This gives us:

$\frac{a x}{a} = \frac{5}{a}$

Simplifying the equation, we get:

$x = \frac{5}{a}$

Conclusion

Therefore, the solution to the equation $a x + 7 = 12$ is $x = \frac{5}{a}$. This means that the value of $x$ is equal to $\frac{5}{a}$.

Comparison with Answer Choices

Let's compare our solution with the answer choices given:

A. $5 - a$ B. $\frac{5}{a}$ C. $\frac{19}{a}$ D. $19 + a$

Our solution matches answer choice B, which is $\frac{5}{a}$.

Final Answer

The final answer is $\boxed{\frac{5}{a}}$.

Step-by-Step Solution

Here's a step-by-step solution to the problem:

1. Start with the given equation: $a x + 7 = 12$
2. Subtract $7$ from both sides of the equation: $a x + 7 - 7 = 12 - 7$
3. Simplify the equation: $a x = 5$
4. Divide both sides of the equation by $a$: $\frac{a x}{a} = \frac{5}{a}$
5. Simplify the equation: $x = \frac{5}{a}$

Tips and Tricks

Here are some tips and tricks to help you solve this problem:

• Make sure to isolate the variable $x$ on one side of the equation.
• Use algebraic operations to simplify the equation and make it easier to solve.
• Pay attention to the signs of the numbers in the equation.
• Use the correct order of operations to evaluate the equation.

Common Mistakes

Here are some common mistakes to avoid when solving this problem:

• Not isolating the variable $x$ on one side of the equation.
• Not using algebraic operations to simplify the equation.
• Not paying attention to the signs of the numbers in the equation.
• Not using the correct order of operations to evaluate the equation.

Real-World Applications

This problem has real-world applications in various fields, such as:

• Algebra: This problem involves solving a linear equation, which is a fundamental concept in algebra.
• Physics: This problem can be used to model real-world situations, such as the motion of an object under the influence of a force.
• Engineering: This problem can be used to design and optimize systems, such as electrical circuits or mechanical systems.

Conclusion

In conclusion, solving the equation $a x + 7 = 12$ involves isolating the variable $x$ on one side of the equation and using algebraic operations to simplify the equation. The solution to the equation is $x = \frac{5}{a}$. This problem has real-world applications in various fields, such as algebra, physics, and engineering.

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Frequently Asked Questions

Q: What is the first step to solve the equation $a x + 7 = 12$?

A: The first step is to isolate the variable $x$ on one side of the equation. To do this, we need to get rid of the constant term $7$ on the left-hand side of the equation.

Q: How do I get rid of the constant term $7$ on the left-hand side of the equation?

A: We can get rid of the constant term $7$ by subtracting $7$ from both sides of the equation. This gives us:

$a x + 7 - 7 = 12 - 7$

Simplifying the equation, we get:

$a x = 5$

Q: What is the next step to solve the equation?

A: Now that we have isolated $x$, we can solve for its value. To do this, we need to get rid of the coefficient $a$ that is being multiplied by $x$. We can do this by dividing both sides of the equation by $a$. This gives us:

$\frac{a x}{a} = \frac{5}{a}$

Simplifying the equation, we get:

$x = \frac{5}{a}$

Q: What is the final answer to the equation?

A: The final answer to the equation $a x + 7 = 12$ is $x = \frac{5}{a}$.

Q: How do I compare my solution with the answer choices?

A: To compare your solution with the answer choices, simply plug in the value of $x$ into each answer choice and see which one matches. In this case, our solution matches answer choice B, which is $\frac{5}{a}$.

Q: What are some common mistakes to avoid when solving this problem?

A: Some common mistakes to avoid when solving this problem include:

• Not isolating the variable $x$ on one side of the equation.
• Not using algebraic operations to simplify the equation.
• Not paying attention to the signs of the numbers in the equation.
• Not using the correct order of operations to evaluate the equation.

Q: What are some real-world applications of this problem?

A: This problem has real-world applications in various fields, such as:

• Algebra: This problem involves solving a linear equation, which is a fundamental concept in algebra.
• Physics: This problem can be used to model real-world situations, such as the motion of an object under the influence of a force.
• Engineering: This problem can be used to design and optimize systems, such as electrical circuits or mechanical systems.

Q: How do I use this problem in a real-world scenario?

A: To use this problem in a real-world scenario, simply substitute the values of $a$ and $x$ into the equation and solve for the unknown value. For example, if $a = 2$ and $x$ is unknown, we can substitute these values into the equation and solve for $x$.

Q: What are some tips and tricks to help me solve this problem?

A: Some tips and tricks to help you solve this problem include:

• Make sure to isolate the variable $x$ on one side of the equation.
• Use algebraic operations to simplify the equation and make it easier to solve.
• Pay attention to the signs of the numbers in the equation.
• Use the correct order of operations to evaluate the equation.

Conclusion

In conclusion, solving the equation $a x + 7 = 12$ involves isolating the variable $x$ on one side of the equation and using algebraic operations to simplify the equation. The solution to the equation is $x = \frac{5}{a}$. This problem has real-world applications in various fields, such as algebra, physics, and engineering. By following the steps outlined in this article, you can solve this problem and apply it to real-world scenarios.