Math / Algebra

QuestionSolve. $\frac{6}{5}+\frac{1}{4}=\frac{1}{x}$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is $\{x \mid x$ is a real number and $x \neq$ $\square$ \}. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. The solution(s) is/are $\square$ . (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) C. There is no solution.

Studdy Solution

STEP 1

What is this asking? We need to find the value of $x$ that makes this equation true! Watch out! Remember, we can't divide by zero, so keep an eye on that $x$ in the denominator!

STEP 2

1. Combine the fractions on the left side.
2. Solve for $x$ .

STEP 3

We've got $\frac{6}{5}$ and $\frac{1}{4}$ , so we need a common denominator.
The smallest number that both 5 and 4 divide into is 20.
Let's get those fractions in terms of twentieths!

STEP 4

To turn $\frac{6}{5}$ into twentieths, we multiply by $\frac{4}{4}$ (which is just a fancy way of writing one).
This gives us $\frac{6}{5} \cdot \frac{4}{4} = \frac{6 \cdot 4}{5 \cdot 4} = \frac{24}{20}$ .
Similarly, for $\frac{1}{4}$ , we multiply by $\frac{5}{5}$ (another fancy one) to get $\frac{1}{4} \cdot \frac{5}{5} = \frac{1 \cdot 5}{4 \cdot 5} = \frac{5}{20}$ .

STEP 5

Now we have $\frac{24}{20} + \frac{5}{20}$ .
Since the denominators are the same, we can just add the numerators: $\frac{24 + 5}{20} = \frac{29}{20}$ .
So, the left side of our original equation simplifies to $\frac{29}{20}$ !

STEP 6

Our equation now looks like this: $\frac{29}{20} = \frac{1}{x}$ .

STEP 7

To get $x$ by itself, we can take the reciprocal of both sides.
Remember, the reciprocal of a fraction just flips it upside down!
So, the reciprocal of $\frac{29}{20}$ is $\frac{20}{29}$ , and the reciprocal of $\frac{1}{x}$ is $\frac{x}{1}$ , which is just $x$ .

STEP 8

So, we have $x = \frac{20}{29}$ !
Boom!

STEP 9

The solution is $x = \frac{20}{29}$ .
This means the correct answer is B, and we fill in the box with $\frac{20}{29}$ .

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Studdy Solution

STEP 1

What is this asking? We need to find the value of $x$ that makes this equation true! Watch out! Remember, we can't divide by zero, so keep an eye on that $x$ in the denominator!

STEP 2

1. Combine the fractions on the left side.
2. Solve for $x$ .

STEP 3

We've got $\frac{6}{5}$ and $\frac{1}{4}$ , so we need a common denominator.
The smallest number that both 5 and 4 divide into is 20.
Let's get those fractions in terms of twentieths!

STEP 4

STEP 5

Now we have $\frac{24}{20} + \frac{5}{20}$ .
Since the denominators are the same, we can just add the numerators: $\frac{24 + 5}{20} = \frac{29}{20}$ .
So, the left side of our original equation simplifies to $\frac{29}{20}$ !

STEP 6

Our equation now looks like this: $\frac{29}{20} = \frac{1}{x}$ .

STEP 7

To get $x$ by itself, we can take the reciprocal of both sides.
Remember, the reciprocal of a fraction just flips it upside down!
So, the reciprocal of $\frac{29}{20}$ is $\frac{20}{29}$ , and the reciprocal of $\frac{1}{x}$ is $\frac{x}{1}$ , which is just $x$ .

STEP 8

So, we have $x = \frac{20}{29}$ !
Boom!

STEP 9

The solution is $x = \frac{20}{29}$ .
This means the correct answer is B, and we fill in the box with $\frac{20}{29}$ .

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Studdy Solution

STEP 1

What is this asking? We need to find the value of xxx that makes this equation true! Watch out! Remember, we can't divide by zero, so keep an eye on that xxx in the denominator!

STEP 2

1. Combine the fractions on the left side.2. Solve for xxx.

STEP 3

We've got 65\frac{6}{5}56​ and 14\frac{1}{4}41​, so we need a common denominator.The smallest number that both 5 and 4 divide into is **20**.Let's get those fractions in terms of twentieths!

STEP 4

STEP 5

Now we have 2420+520\frac{24}{20} + \frac{5}{20}2024​+205​.Since the denominators are the same, we can just add the numerators: 24+520=2920\frac{24 + 5}{20} = \frac{29}{20}2024+5​=2029​.So, the left side of our original equation simplifies to 2920\frac{29}{20}2029​!

STEP 6

Our equation now looks like this: 2920=1x\frac{29}{20} = \frac{1}{x}2029​=x1​.

STEP 7

To get xxx by itself, we can take the reciprocal of both sides.Remember, the reciprocal of a fraction just flips it upside down!So, the reciprocal of 2920\frac{29}{20}2029​ is 2029\frac{20}{29}2920​, and the reciprocal of 1x\frac{1}{x}x1​ is x1\frac{x}{1}1x​, which is just xxx.

STEP 8

So, we have x=2029x = \frac{20}{29}x=2920​!Boom!

STEP 9

The solution is x=2029x = \frac{20}{29}x=2920​.This means the correct answer is B, and we fill in the box with 2029\frac{20}{29}2920​.

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Studdy solves anything!

Start learning now

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What is this asking? We need to find the value of $x$ that makes this equation true! Watch out! Remember, we can't divide by zero, so keep an eye on that $x$ in the denominator!

1. Combine the fractions on the left side.
2. Solve for $x$ .

We've got $\frac{6}{5}$ and $\frac{1}{4}$ , so we need a common denominator.
The smallest number that both 5 and 4 divide into is 20.
Let's get those fractions in terms of twentieths!

Now we have $\frac{24}{20} + \frac{5}{20}$ .
Since the denominators are the same, we can just add the numerators: $\frac{24 + 5}{20} = \frac{29}{20}$ .
So, the left side of our original equation simplifies to $\frac{29}{20}$ !

Our equation now looks like this: $\frac{29}{20} = \frac{1}{x}$ .

To get $x$ by itself, we can take the reciprocal of both sides.
Remember, the reciprocal of a fraction just flips it upside down!
So, the reciprocal of $\frac{29}{20}$ is $\frac{20}{29}$ , and the reciprocal of $\frac{1}{x}$ is $\frac{x}{1}$ , which is just $x$ .

So, we have $x = \frac{20}{29}$ !
Boom!

The solution is $x = \frac{20}{29}$ .
This means the correct answer is B, and we fill in the box with $\frac{20}{29}$ .