Responses

Question

Start Fraction x over 3.2 End Fraction equals 1.8 and 1.8x equals 3.2

negative Start Fraction 3 over 4 End Fraction x equals Start Fraction 5 over 2 End Fraction and Start Fraction 5 over 2 End Fraction x equals negative Start Fraction 3 over 4 End Fraction

Start Fraction 3 over 8 End Fraction x equals 1 and Start Fraction 1 over 3 End Fraction x equals Start Fraction 1 over 8 End Fraction

negative 3.2x equals 0.64 and Start Fraction x over 4 End Fraction equals negative 0.05

Answer 1

It looks like you have a series of equations. Let's solve each one for \( x \):

1. First Pair of Equations: \[ \frac{x}{3.2} = 1.8 \] To solve for \( x \), multiply both sides by \( 3.2 \): \[ x = 1.8 \times 3.2 \] \[ x = 5.76 \]

   Now for the second equation: \[ 1.8x = 3.2 \] Divide both sides by \( 1.8 \): \[ x = \frac{3.2}{1.8} \] \[ x \approx 1.78 \]

2. Second Pair of Equations: \[ -\frac{3}{4}x = \frac{5}{2} \] Multiply both sides by \(-\frac{4}{3}\): \[ x = -\frac{5}{2} \times -\frac{4}{3} = \frac{20}{6} = \frac{10}{3} \approx 3.33 \]

   Now for the second equation: \[ \frac{5}{2}x = -\frac{3}{4} \] Multiply both sides by \(\frac{2}{5}\): \[ x = -\frac{3}{4} \times \frac{2}{5} = -\frac{3}{10} = -0.3 \]

3. Third Pair of Equations: \[ \frac{3}{8}x = 1 \] Multiply both sides by \(\frac{8}{3}\): \[ x = 1 \times \frac{8}{3} = \frac{8}{3} \approx 2.67 \]

   Now for the second equation: \[ \frac{1}{3}x = \frac{1}{8} \] Multiply both sides by \(3\): \[ x = \frac{3}{8} = 0.375 \]

4. Fourth Pair of Equations: \[ -3.2x = 0.64 \] Divide both sides by \(-3.2\): \[ x = \frac{0.64}{-3.2} = -0.2 \]

   Now for the second equation: \[ \frac{x}{4} = -0.05 \] Multiply both sides by \(4\): \[ x = -0.05 \times 4 = -0.2 \]

Summary of Solutions:

1. \( x \) from \(\frac{x}{3.2} = 1.8\): \( 5.76 \)
   \(1.8x = 3.2\): \( 1.78 \)

2. \( x \) from \(-\frac{3}{4}x = \frac{5}{2}\): \( \frac{10}{3} \)
   \( \frac{5}{2}x = -\frac{3}{4}\): \(-0.3\)

3. \( x \) from \(\frac{3}{8}x = 1\): \( \frac{8}{3} \)
   \( \frac{1}{3}x = \frac{1}{8}\): \(0.375\)

4. \( x \) from \(-3.2x = 0.64\): \(-0.2\)
   \( \frac{x}{4} = -0.05\): \(-0.2\)

Feel free to ask if you need anything else!

Answer 2

so which one is it and why

Answer 3

It looks like you have multiple equations, each of which can yield a different solution for \( x \). I'll clarify each case to avoid confusion:

1. First Pair of Equations:

   • From \( \frac{x}{3.2} = 1.8 \), we found \( x = 5.76 \).
   • From \( 1.8x = 3.2 \), we found \( x \approx 1.78 \).

   Conclusion: These equations represent different scenarios, leading to different values for \( x \). They are not the same equation.

2. Second Pair of Equations:

   • From \( -\frac{3}{4}x = \frac{5}{2} \), we found \( x \approx 3.33 \).
   • From \( \frac{5}{2}x = -\frac{3}{4} \), we found \( x = -0.3 \).

   Conclusion: Again, these two equations provide different values for \( x \).

3. Third Pair of Equations:

   • From \( \frac{3}{8}x = 1 \), we found \( x \approx 2.67 \).
   • From \( \frac{1}{3}x = \frac{1}{8} \), we found \( x = 0.375 \).

   Conclusion: Different values for \( x \) again suggest distinct scenarios.

4. Fourth Pair of Equations:

   • From \( -3.2x = 0.64 \), we found \( x = -0.2 \).
   • From \( \frac{x}{4} = -0.05 \), we also found \( x = -0.2 \).

   Conclusion: For this pair, both equations yield the same solution, \( x = -0.2 \).

So, Which One Is It?

• The equations you provided are independent of one another, meaning each pair can represent different scenarios or problems.
• If you are looking for a single value of \( x \), you need to specify which equation you want to solve.

Final Note:

If you need a specific value for a certain equation or if there is a certain context (like a problem statement) that leads you to choose one over another, please provide that context, and I can help you further!

Answer 4

can you show the steps for doing number 4

Answer 5

Sure! Let's solve each equation in the fourth pair step by step:

Fourth Pair of Equations

1. First Equation:

\[ -3.2x = 0.64 \]

Step 1: Isolate \( x \)

To do this, divide both sides by \(-3.2\): \[ x = \frac{0.64}{-3.2} \]

Step 2: Perform the Division

Now, let's calculate \(\frac{0.64}{-3.2}\): \[ 0.64 \div -3.2 = -0.2 \]

So, \[ x = -0.2 \]

2. Second Equation:

\[ \frac{x}{4} = -0.05 \]

Step 1: Isolate \( x \)

To isolate \( x \), multiply both sides by \( 4 \): \[ x = -0.05 \times 4 \]

Step 2: Perform the Multiplication \[ x = -0.2 \]

Summary of Solutions for Number 4

• For the first equation \( -3.2x = 0.64 \), we found \( x = -0.2 \).
• For the second equation \( \frac{x}{4} = -0.05 \), we also found \( x = -0.2 \).

Both equations give the same solution: \[ \boxed{-0.2} \]

If you have any further questions or need clarification on any steps, feel free to ask!