Solve This Equation: $3x - \frac{1}{5} - \frac{2}{9}x = \frac{124}{5}$Step 1: Simplify By Combining Like Terms. Which Terms Can Be Combined? $3x - \frac{1}{5} - \frac{2}{9}x = \frac{124}{5}$

**Solve this Equation: A Step-by-Step Guide** =====================================================

Step 1: Simplify by Combining Like Terms

The given equation is $3x - \frac{1}{5} - \frac{2}{9}x = \frac{124}{5}$. To simplify this equation, we need to combine like terms. Like terms are the terms that have the same variable raised to the same power.

In this equation, the like terms are the terms with the variable $x$. The terms with the variable $x$ are $3x$ and $-\frac{2}{9}x$. We can combine these two terms by adding or subtracting their coefficients.

Q: What are the coefficients of the like terms? A: The coefficient of $3x$ is $3$ and the coefficient of $-\frac{2}{9}x$ is $-\frac{2}{9}$.

Q: How do we combine the like terms? A: To combine the like terms, we add or subtract their coefficients. In this case, we add the coefficients of $3x$ and $-\frac{2}{9}x$.

Step 2: Combine the Like Terms

To combine the like terms, we add the coefficients of $3x$ and $-\frac{2}{9}x$. This gives us:

$3x - \frac{2}{9}x = \left(3 - \frac{2}{9}\right)x$

Q: What is the value of $\left(3 - \frac{2}{9}\right)$? A: To find the value of $\left(3 - \frac{2}{9}\right)$, we need to subtract $\frac{2}{9}$ from $3$. We can do this by finding a common denominator, which is $9$. Then, we can subtract the numerators:

$\left(3 - \frac{2}{9}\right) = \frac{27}{9} - \frac{2}{9} = \frac{25}{9}$

Q: What is the simplified equation? A: The simplified equation is:

$\frac{25}{9}x - \frac{1}{5} = \frac{124}{5}$

Step 3: Isolate the Variable

To isolate the variable $x$, we need to get rid of the constant term $-\frac{1}{5}$. We can do this by adding $\frac{1}{5}$ to both sides of the equation.

Q: What is the value of $\frac{1}{5} + \frac{1}{5}$? A: To find the value of $\frac{1}{5} + \frac{1}{5}$, we can add the numerators:

$\frac{1}{5} + \frac{1}{5} = \frac{2}{5}$

Q: What is the equation after adding $\frac{1}{5}$ to both sides? A: The equation after adding $\frac{1}{5}$ to both sides is:

$\frac{25}{9}x = \frac{124}{5} + \frac{2}{5}$

Q: What is the value of $\frac{124}{5} + \frac{2}{5}$? A: To find the value of $\frac{124}{5} + \frac{2}{5}$, we can add the numerators:

$\frac{124}{5} + \frac{2}{5} = \frac{126}{5}$

Q: What is the equation after adding $\frac{2}{5}$ to $\frac{124}{5}$? A: The equation after adding $\frac{2}{5}$ to $\frac{124}{5}$ is:

$\frac{25}{9}x = \frac{126}{5}$

Step 4: Solve for $x$

To solve for $x$, we need to get rid of the coefficient $\frac{25}{9}$. We can do this by multiplying both sides of the equation by the reciprocal of $\frac{25}{9}$, which is $\frac{9}{25}$.

Q: What is the value of $\frac{9}{25} \times \frac{25}{9}$? A: To find the value of $\frac{9}{25} \times \frac{25}{9}$, we can multiply the numerators and denominators:

$\frac{9}{25} \times \frac{25}{9} = \frac{9 \times 25}{25 \times 9} = 1$

Q: What is the equation after multiplying both sides by $\frac{9}{25}$? A: The equation after multiplying both sides by $\frac{9}{25}$ is:

$x = \frac{126}{5} \times \frac{9}{25}$

Q: What is the value of $\frac{126}{5} \times \frac{9}{25}$? A: To find the value of $\frac{126}{5} \times \frac{9}{25}$, we can multiply the numerators and denominators:

$\frac{126}{5} \times \frac{9}{25} = \frac{126 \times 9}{5 \times 25} = \frac{1134}{125}$

Q: What is the value of $x$? A: The value of $x$ is $\frac{1134}{125}$.

Conclusion

In this article, we solved the equation $3x - \frac{1}{5} - \frac{2}{9}x = \frac{124}{5}$ by simplifying by combining like terms, isolating the variable, and solving for $x$. We found that the value of $x$ is $\frac{1134}{125}$.