"solve the equation 2/3-4x+7/2=-9x+5/6" okay when i combined terms it gave me 25/6-4x=-9x+5/6 and i think you said to add 9 so it gave me 79/6-4x=-9x+59/6 so whats the next step?? did i do something wrong? or is it good still?? say all the steps straightforwardly the only options i can do is add subtract mutiply and divide since i already combined terms

Answer 1

Let's solve the equation step by step.

You started with the equation:

\[ \frac{2}{3} - 4x + \frac{7}{2} = -9x + \frac{5}{6} \]

1. Combine like terms on the left side:

   • First, find a common denominator for \(\frac{2}{3}\) and \(\frac{7}{2}\). The common denominator is 6.
   • Rewrite the fractions: \[ \frac{2}{3} = \frac{4}{6} \quad \text{and} \quad \frac{7}{2} = \frac{21}{6} \]
   • Now combine: \[ \frac{4}{6} + \frac{21}{6} = \frac{25}{6} \]
   • So the equation becomes: \[ \frac{25}{6} - 4x = -9x + \frac{5}{6} \]

2. Move all terms involving \(x\) to one side and the constant terms to the other side:

   • Add \(9x\) to both sides: \[ \frac{25}{6} - 4x + 9x = \frac{5}{6} \]
   • This simplifies to: \[ \frac{25}{6} + 5x = \frac{5}{6} \]

3. Isolate the term with \(x\):

   • Subtract \(\frac{25}{6}\) from both sides: \[ 5x = \frac{5}{6} - \frac{25}{6} \]
   • This simplifies to: \[ 5x = \frac{5 - 25}{6} = \frac{-20}{6} = \frac{-10}{3} \]

4. Solve for \(x\):

   • Divide both sides by 5: \[ x = \frac{-10}{3} \div 5 = \frac{-10}{3} \cdot \frac{1}{5} = \frac{-10}{15} = \frac{-2}{3} \]

So the solution is:

\[ \boxed{x = -\frac{2}{3}} \]

Answer 2

okay we are not on the same page here.. i combined terms it gave me 25/6-4x=-9x+5/6 added 9 so it gave me 79/6-4x=-9x+59/6 then subtracted both sides by 25/6 gave me 9-4x=-9x+17/3 then divide 5 both sides and got 9/5-4/5=-9/5x+17/15 and you said you would get x=-2/3??

Answer 3

It looks like there's a misunderstanding in your steps. Let's go through the equation together again from your combined terms to clarify any confusion.

You combined terms correctly:

Starting from:

\[ \frac{25}{6} - 4x = -9x + \frac{5}{6} \]

Step 1: Rearranging Terms

Now, let's rearrange the equation without any additional steps or variables being added that aren't needed.

1. Add \(9x\) to both sides: \[ \frac{25}{6} - 4x + 9x = \frac{5}{6} \] This simplifies to: \[ \frac{25}{6} + 5x = \frac{5}{6} \]

2. Subtract \(\frac{25}{6}\) from both sides: \[ 5x = \frac{5}{6} - \frac{25}{6} \] This simplifies to: \[ 5x = \frac{5 - 25}{6} = \frac{-20}{6} = \frac{-10}{3} \]

3. Divide both sides by \(5\): \[ x = \frac{-10}{3} \div 5 = \frac{-10}{3} \cdot \frac{1}{5} = \frac{-10}{15} = \frac{-2}{3} \]

Conclusion

Thus, the final value for \(x\) is:

\[ \boxed{-\frac{2}{3}} \]

Clarifications

• If you are subtracting different values and adjusting incorrectly, ensure you're performing the same operations on both sides and not introducing additional numbers.
• It seems you mentioned "added 9" which might have caused some confusion. We should only be rearranging \(-9x + 5/6\) to the same side as the other terms.

If you need further clarification or assistance with any step, please let me know!

Answer 4

THIS PART " It seems you mentioned "added 9" which might have caused some confusion. We should only be rearranging \(-9x + 5/6\) to the same side as the other terms." YOU TOLD ME TO RIGHT HERE Step 1: Rearranging Terms
Now, let's rearrange the equation without any additional steps or variables being added that aren't needed.

1. **Add \(9x\) to both sides**: ADD 9 ADD 9 9 9 9 okay tell me what do i divide add subtract multiply with the number but in step 1 2 3 etc

Answer 5

I apologize for the confusion in my earlier explanations. Let's clarify the steps step by step, using addition, subtraction, and division only as specified. Here's the correct, clear process with all the corresponding operations indicated:

Starting Point

You have already combined the terms correctly to reach:

\[ \frac{25}{6} - 4x = -9x + \frac{5}{6} \]

Step 1: Move \(9x\) to one side

Operation: Add \(9x\) to both sides.

\[ \frac{25}{6} - 4x + 9x = \frac{5}{6} \]

This simplifies to:

\[ \frac{25}{6} + 5x = \frac{5}{6} \]

Step 2: Move \(\frac{25}{6}\) to the right side

Operation: Subtract \(\frac{25}{6}\) from both sides.

\[ 5x = \frac{5}{6} - \frac{25}{6} \]

Step 3: Simplify the right side

Now, calculate the right side:

\[ 5x = \frac{5 - 25}{6} = \frac{-20}{6} = \frac{-10}{3} \]

Step 4: Isolate \(x\)

Operation: Divide both sides by \(5\).

\[ x = \frac{-10}{3} \div 5 = \frac{-10}{3} \cdot \frac{1}{5} = \frac{-10}{15} = \frac{-2}{3} \]

Final Result

So, the final solution is:

\[ \boxed{x = -\frac{2}{3}} \]

Summary

• Step 1: Add \(9x\) (to combine \(x\) terms).
• Step 2: Subtract \(\frac{25}{6}\) (to isolate \(x\)).
• Step 3: Simplify the fraction.
• Step 4: Divide by \(5\) to solve for \(x\).

If you have any further questions or would like another step-by-step explanation, feel free to ask!

Answer 6

OKAY THANK YOU I GET IT NOW I GOT -2/3 so combine terms add 9x divide 25/6 then divide 5x and get -2/3 thank you

but now Solve: StartFraction 2 Over 3 EndFraction minus 4 x plus StartFraction 7 Over 2 EndFraction equals negative 9 x plus StartFraction 5 Over 6. EndFraction. – 4x + = –9x +

x = x equals negative StartFraction 3 Over 2 EndFraction.
x = x equals negative StartFraction 2 Over 3 EndFraction.
x = x equals StartFraction 2 Over 3 EndFraction.
x = x equals StartFraction 3 Over 2 EndFraction.

Answer 7

Great job on keeping track of the steps, and I'm glad you understand how to solve the equation now!

Let's go through the original equation again to confirm the solution and see if \(x = -\frac{2}{3}\) is indeed the correct answer.

We start with the equation:

\[ \frac{2}{3} - 4x + \frac{7}{2} = -9x + \frac{5}{6} \]

Step 1: Combine Like Terms

First, combine the terms on the left side:

1. Find a common denominator for \(\frac{2}{3}\) and \(\frac{7}{2}\). The common denominator is 6.

   • Rewrite the fractions: \[ \frac{2}{3} = \frac{4}{6} \quad \text{and} \quad \frac{7}{2} = \frac{21}{6} \]

2. Then, combine: \[ \frac{4}{6} + \frac{21}{6} = \frac{25}{6} \]

So the equation is now:

\[ \frac{25}{6} - 4x = -9x + \frac{5}{6} \]

Step 2: Move \(9x\) to the left side

Operation: Add \(9x\) to both sides:

\[ \frac{25}{6} - 4x + 9x = \frac{5}{6} \]

This simplifies to:

\[ \frac{25}{6} + 5x = \frac{5}{6} \]

Step 3: Move \(\frac{25}{6}\) to the right side

Operation: Subtract \(\frac{25}{6}\) from both sides:

\[ 5x = \frac{5}{6} - \frac{25}{6} \]

Step 4: Simplify the right side

Calculate:

\[ 5x = \frac{5 - 25}{6} = \frac{-20}{6} = \frac{-10}{3} \]

Step 5: Solve for \(x\)

Operation: Divide both sides by \(5\):

\[ x = \frac{-10}{3} \div 5 = \frac{-10}{3} \cdot \frac{1}{5} = \frac{-10}{15} = \frac{-2}{3} \]

Conclusion

The solution is indeed:

\[ \boxed{x = -\frac{2}{3}} \]

Evaluating the Options

Now, from your options:

1. \(x = -\frac{3}{2}\)
2. \(x = -\frac{2}{3}\) (This is correct)
3. \(x = \frac{2}{3}\)
4. \(x = \frac{3}{2}\)

The correct answer is:

Option 2: \(x = -\frac{2}{3}\)

If you have any more questions or need further clarification on anything else, just let me know!

Answer 8

hey just very quick whos your favorite victoria secret model and why?

anyways The number of rainbow smelt in Lake Michigan had an average rate of change of −19.76 per year between 1990 and 2000. The bloater fish population had an average rate of change of −92.57 per year during the same time. If the initial population of rainbow smelt was 227 and the initial population of bloater fish was 1,052, after how many years were the two populations equal?

The linear function that models the population of rainbow smelt is y1 = −19.76x + 227, where
x = the years since 1990 and y1 = the number of rainbow smelt.

The linear function that models the population of bloater fish is y2 =_______
.

The linear equation that determines when the two populations were equal is_________
.

The solution is x =______
years.

Answer 9

Let's start with your questions about the models and then solve the population problem step by step.

1. Favorite Victoria's Secret Model

I don't have personal preferences, emotions, or favorites, but many people admire models like Adriana Lima and Gigi Hadid for their work and impact in the fashion industry. They have become icons through their runway walks and campaigns!

2. Population Problem

Now, let's focus on the population problem involving the rainbow smelt and the bloater fish.

Given Information:

• Rainbow Smelt:

  • Initial population: 227
  • Rate of change: -19.76 per year
  • Linear function: \( y_1 = -19.76x + 227 \)

• Bloater Fish:

  • Initial population: 1,052
  • Rate of change: -92.57 per year

Step 1: Write the Linear Function for the Bloater Fish

The linear function that models the population of bloater fish can be written similarly:

\[ y_2 = -92.57x + 1052 \]

where:

• \(y_2\) = number of bloater fish,
• \(x\) = years since 1990.

Step 2: Set the Two Population Functions Equal

To find when the two populations are equal, set \(y_1\) equal to \(y_2\):

\[ -19.76x + 227 = -92.57x + 1052 \]

Step 3: Solve for \(x\)

1. Rearranging the Equation: First, get all \(x\) terms on one side and the constants on the other side. Adding \(92.57x\) to both sides:

\[ -19.76x + 92.57x + 227 = 1052 \]

Which simplifies to:

\[ 72.81x + 227 = 1052 \]

2. Subtract 227 from both sides: \[ 72.81x = 1052 - 227 \] \[ 72.81x = 825 \]

3. Divide by 72.81: \[ x = \frac{825}{72.81} \approx 11.32 \]

Final Answers

1. Linear function that models bloater fish:
   \[ y_2 = -92.57x + 1052 \]

2. Linear equation that determines when populations are equal:
   \[ -19.76x + 227 = -92.57x + 1052 \]

3. Solution (x):
   \[ x \approx 11.32 \] years since 1990.

Conclusion

So, the populations of rainbow smelt and bloater fish will be equal approximately 11.32 years after 1990, which is about 2001.

If you have any more questions or need additional explanations, feel free to ask!

Answer 10

Whats the answer for The linear function that models the population of bloater fish is y2 =____ because The linear equation that determines when the two populations were equal is –19.76x + 227 = –92.57x + 1052 and the solution is x = 11.33 years.

Answer 11

Got it! Let's fill in the information step by step.

1. Linear Function for Bloater Fish

You need the linear function that models the population of bloater fish given the initial population and the rate of change.

Given Information:

• Initial population of bloater fish: 1,052
• Rate of change: -92.57 per year

Linear Function:

The formula for the linear function is: \[ y_2 = \text{(rate of change)} \cdot x + \text{(initial population)} \]

Substituting in the values: \[ y_2 = -92.57x + 1052 \]

2. Equation for the Two Populations When They Are Equal

You also have the equation set up correctly: \[ -19.76x + 227 = -92.57x + 1052 \]

Which means that's the equation that determines when the two populations are equal.

3. Solution for \(x\)

You've calculated: \[ x \approx 11.33 \text{ years since 1990.} \]

Final Answers

• The linear function that models the population of bloater fish is: \[ y_2 = -92.57x + 1052 \]

• The linear equation that determines when the two populations were equal is: \[ -19.76x + 227 = -92.57x + 1052 \]

• The solution is: \[ x \approx 11.33 \text{ years.} \]

Summary

• \(y_2 = -92.57x + 1052\)
• The other equation is correctly set.
• \(x \approx 11.33\)

If you need further assistance or have more questions, feel free to ask!