Question
3x-1/5-2/9x=124/5 simplified by combining like terms are 3x and -2/9x
now isolate the variable term by adding this value to both sides of the equation and its 1/5 now multiply by this number to make the coeffecient of the variable 1: 9/25 or 3 or 25/9
now isolate the variable term by adding this value to both sides of the equation and its 1/5 now multiply by this number to make the coeffecient of the variable 1: 9/25 or 3 or 25/9
Answers
GPT-4o mini
Let's simplify and solve the equation step by step:
1. Start with the original equation:
\[
3x - \frac{1}{5} - \frac{2}{9}x = \frac{124}{5}
\]
2. Combine like terms. The terms containing \(x\) are \(3x\) and \(-\frac{2}{9}x\). To combine these, we need a common denominator. The least common multiple of the denominators \(1\) and \(9\) is \(9\):
\[
3x = \frac{27}{9}x
\]
Now we can combine:
\[
\frac{27}{9}x - \frac{2}{9}x = \frac{27 - 2}{9}x = \frac{25}{9}x
\]
So, we can rewrite the equation as:
\[
\frac{25}{9}x - \frac{1}{5} = \frac{124}{5}
\]
3. Next, let's isolate the variable term by adding \(\frac{1}{5}\) to both sides:
\[
\frac{25}{9}x = \frac{124}{5} + \frac{1}{5}
\]
\[
\frac{25}{9}x = \frac{124 + 1}{5} = \frac{125}{5} = 25
\]
4. Now, to isolate \(x\), we multiply both sides of the equation by the reciprocal of \(\frac{25}{9}\), which is \(\frac{9}{25}\):
\[
x = 25 \cdot \frac{9}{25}
\]
\[
x = 9
\]
So the solution to the equation is:
\[
\boxed{9}
\]
1. Start with the original equation:
\[
3x - \frac{1}{5} - \frac{2}{9}x = \frac{124}{5}
\]
2. Combine like terms. The terms containing \(x\) are \(3x\) and \(-\frac{2}{9}x\). To combine these, we need a common denominator. The least common multiple of the denominators \(1\) and \(9\) is \(9\):
\[
3x = \frac{27}{9}x
\]
Now we can combine:
\[
\frac{27}{9}x - \frac{2}{9}x = \frac{27 - 2}{9}x = \frac{25}{9}x
\]
So, we can rewrite the equation as:
\[
\frac{25}{9}x - \frac{1}{5} = \frac{124}{5}
\]
3. Next, let's isolate the variable term by adding \(\frac{1}{5}\) to both sides:
\[
\frac{25}{9}x = \frac{124}{5} + \frac{1}{5}
\]
\[
\frac{25}{9}x = \frac{124 + 1}{5} = \frac{125}{5} = 25
\]
4. Now, to isolate \(x\), we multiply both sides of the equation by the reciprocal of \(\frac{25}{9}\), which is \(\frac{9}{25}\):
\[
x = 25 \cdot \frac{9}{25}
\]
\[
x = 9
\]
So the solution to the equation is:
\[
\boxed{9}
\]
ITS 3x and -2/9x THEN 1/5 AND 9/25
GPT-4o mini
Got it! Let's retake the equation \(3x - \frac{1}{5} - \frac{2}{9}x = \frac{124}{5}\) and simplify it step by step using the terms you've highlighted: \(3x\), \(-\frac{2}{9}x\), along with \( -\frac{1}{5} \).
### Step 1: Combine Like Terms
Starting with the equation:
\[
3x - \frac{2}{9}x - \frac{1}{5} = \frac{124}{5}
\]
1. Convert \(3x\) to the same denominator (\(9\)):
\[
3x = \frac{27}{9}x
\]
2. Now combine \( \frac{27}{9}x\) and \(-\frac{2}{9}x\):
\[
\frac{27}{9}x - \frac{2}{9}x = \frac{25}{9}x
\]
So the equation simplifies to:
\[
\frac{25}{9}x - \frac{1}{5} = \frac{124}{5}
\]
### Step 2: Isolate the Variable
Next, we add \(\frac{1}{5}\) to both sides of the equation:
\[
\frac{25}{9}x = \frac{124}{5} + \frac{1}{5}
\]
This simplifies to:
\[
\frac{25}{9}x = \frac{124 + 1}{5} = \frac{125}{5} = 25
\]
### Step 3: Solve for \(x\)
Now we need to isolate \(x\) by multiplying both sides by the reciprocal of \(\frac{25}{9}\), which is \(\frac{9}{25}\):
\[
x = 25 \cdot \frac{9}{25}
\]
The \(25\) in the numerator and denominator cancel out, giving:
\[
x = 9
\]
### Conclusion
So, the final solution is:
\[
\boxed{9}
\]
If you're referring to another way of representing the coefficient or the operation regarding \(1/5\) and \(9/25\), please clarify!
### Step 1: Combine Like Terms
Starting with the equation:
\[
3x - \frac{2}{9}x - \frac{1}{5} = \frac{124}{5}
\]
1. Convert \(3x\) to the same denominator (\(9\)):
\[
3x = \frac{27}{9}x
\]
2. Now combine \( \frac{27}{9}x\) and \(-\frac{2}{9}x\):
\[
\frac{27}{9}x - \frac{2}{9}x = \frac{25}{9}x
\]
So the equation simplifies to:
\[
\frac{25}{9}x - \frac{1}{5} = \frac{124}{5}
\]
### Step 2: Isolate the Variable
Next, we add \(\frac{1}{5}\) to both sides of the equation:
\[
\frac{25}{9}x = \frac{124}{5} + \frac{1}{5}
\]
This simplifies to:
\[
\frac{25}{9}x = \frac{124 + 1}{5} = \frac{125}{5} = 25
\]
### Step 3: Solve for \(x\)
Now we need to isolate \(x\) by multiplying both sides by the reciprocal of \(\frac{25}{9}\), which is \(\frac{9}{25}\):
\[
x = 25 \cdot \frac{9}{25}
\]
The \(25\) in the numerator and denominator cancel out, giving:
\[
x = 9
\]
### Conclusion
So, the final solution is:
\[
\boxed{9}
\]
If you're referring to another way of representing the coefficient or the operation regarding \(1/5\) and \(9/25\), please clarify!