Solve For X To The Nearest Tenth.Given: ${ \frac{7}{x} = 10 }$

Mar 12, 2025 by ADMIN 64 views

Solve for x to the nearest tenth

Understanding the Problem

To solve for x to the nearest tenth, we need to isolate the variable x in the given equation. The equation provided is $\frac{7}{x} = 10$ . Our goal is to find the value of x that satisfies this equation.

Isolating the Variable

To isolate x, we can start by multiplying both sides of the equation by x. This will eliminate the fraction and allow us to work with a simpler equation. The equation becomes:

7 = 10x

Solving for x

Now that we have the equation $7 = 10x$ , we can solve for x by dividing both sides of the equation by 10. This will give us the value of x.

x = \frac{7}{10}

Rounding to the Nearest Tenth

Since we are asked to solve for x to the nearest tenth, we need to round our answer to one decimal place. The value of x is $\frac{7}{10}$ , which is equal to 0.7. Therefore, the value of x to the nearest tenth is 0.7.

Checking the Answer

To check our answer, we can substitute x = 0.7 back into the original equation and see if it is true. The original equation is $\frac{7}{x} = 10$ . Substituting x = 0.7, we get:

\frac{7}{0.7} = 10

Simplifying the left-hand side of the equation, we get:

10 = 10

This shows that our answer is correct.

Conclusion

In this problem, we were given the equation $\frac{7}{x} = 10$ and asked to solve for x to the nearest tenth. We isolated the variable x by multiplying both sides of the equation by x, and then solved for x by dividing both sides of the equation by 10. Our answer was x = 0.7, which we rounded to the nearest tenth. We checked our answer by substituting x = 0.7 back into the original equation and found that it was true.

Real-World Applications

Solving for x to the nearest tenth has many real-world applications. For example, in physics, we often need to solve equations involving fractions to find the value of a variable. In engineering, we may need to solve equations involving fractions to design and build complex systems. In finance, we may need to solve equations involving fractions to calculate interest rates and investment returns.

Tips and Tricks

When solving for x to the nearest tenth, it's essential to follow the order of operations (PEMDAS) and to be careful when multiplying and dividing fractions. It's also a good idea to check your answer by substituting it back into the original equation.

Common Mistakes

One common mistake when solving for x to the nearest tenth is to round the answer incorrectly. For example, if the answer is 0.67, it's easy to round it to 0.7, but this can lead to incorrect answers. Another common mistake is to forget to check the answer by substituting it back into the original equation.

Summary

Solving for x to the nearest tenth is a fundamental concept in mathematics that has many real-world applications. By following the order of operations and being careful when multiplying and dividing fractions, we can solve for x to the nearest tenth with ease. Remember to check your answer by substituting it back into the original equation to ensure that it's correct.

Final Answer

The final answer is: $\boxed{0.7}$

Frequently Asked Questions

Q: What is the first step in solving for x to the nearest tenth?

A: The first step in solving for x to the nearest tenth is to isolate the variable x in the given equation. This can be done by multiplying both sides of the equation by x, which will eliminate the fraction and allow us to work with a simpler equation.

Q: How do I round my answer to the nearest tenth?

A: To round your answer to the nearest tenth, you need to look at the hundredth place digit. If it's 5 or greater, you round up. If it's 4 or less, you round down. For example, if your answer is 0.67, you would round it to 0.7.

Q: What if I get a decimal answer that doesn't end in .0?

A: If you get a decimal answer that doesn't end in .0, you can still round it to the nearest tenth. For example, if your answer is 0.675, you would round it to 0.7.

Q: Can I use a calculator to solve for x to the nearest tenth?

A: Yes, you can use a calculator to solve for x to the nearest tenth. However, make sure to check your answer by substituting it back into the original equation to ensure that it's correct.

Q: What if I'm given an equation with a variable in the denominator?

A: If you're given an equation with a variable in the denominator, you can still solve for x to the nearest tenth. To do this, multiply both sides of the equation by the denominator to eliminate the fraction.

Q: Can I use a graphing calculator to solve for x to the nearest tenth?

A: Yes, you can use a graphing calculator to solve for x to the nearest tenth. However, make sure to check your answer by substituting it back into the original equation to ensure that it's correct.

Q: What if I'm given an equation with multiple variables?

A: If you're given an equation with multiple variables, you can still solve for x to the nearest tenth. To do this, isolate the variable x by using algebraic manipulations and then solve for x.

Q: Can I use a computer algebra system (CAS) to solve for x to the nearest tenth?

A: Yes, you can use a CAS to solve for x to the nearest tenth. However, make sure to check your answer by substituting it back into the original equation to ensure that it's correct.

Q: What if I'm given an equation with a negative exponent?

A: If you're given an equation with a negative exponent, you can still solve for x to the nearest tenth. To do this, rewrite the equation with a positive exponent by taking the reciprocal of both sides.

Q: Can I use a spreadsheet to solve for x to the nearest tenth?

A: Yes, you can use a spreadsheet to solve for x to the nearest tenth. However, make sure to check your answer by substituting it back into the original equation to ensure that it's correct.

Q: What if I'm given an equation with a trigonometric function?

A: If you're given an equation with a trigonometric function, you can still solve for x to the nearest tenth. To do this, use trigonometric identities and algebraic manipulations to isolate the variable x.

Q: Can I use a graphing software to solve for x to the nearest tenth?

A: Yes, you can use a graphing software to solve for x to the nearest tenth. However, make sure to check your answer by substituting it back into the original equation to ensure that it's correct.

Q: What if I'm given an equation with a logarithmic function?

A: If you're given an equation with a logarithmic function, you can still solve for x to the nearest tenth. To do this, use logarithmic identities and algebraic manipulations to isolate the variable x.