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If x/−5=2 , then what is the value of x ?

9 answers

To solve for \( x \) in the equation

\[ \frac{x}{-5} = 2, \]

you can start by multiplying both sides of the equation by \(-5\) to isolate \( x \):

\[ x = 2 \cdot (-5). \]

Calculating the right side gives:

\[ x = -10. \]

Therefore, the value of \( x \) is

\[ \boxed{-10}. \]

Which of the following pairs of equations has exactly the same solution?(1 point)
Responses

3/8x=1 and 1/3x=1/8
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

−3/4x=5/2 and 5/2x=−3/4
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

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

−3.2x=0.64 and x4=−0.05

To determine which pairs of equations have the same solution, we will solve each pair.

  1. Pair 1: \[ \frac{3}{8}x = 1 \] To solve for \( x \): \[ x = \frac{1}{\frac{3}{8}} = 1 \cdot \frac{8}{3} = \frac{8}{3} \]

    \[ \frac{1}{3}x = \frac{1}{8} \] To solve for \( x \): \[ x = \frac{1}{\frac{1}{3}} \cdot \frac{1}{8} = 3 \cdot \frac{1}{8} = \frac{3}{8} \]

    These equations do not have the same solution.

  2. Pair 2: \[ -\frac{3}{4}x = \frac{5}{2} \] To solve for \( x \): \[ x = \frac{\frac{5}{2}}{-\frac{3}{4}} = \frac{5}{2} \cdot \frac{-4}{3} = -\frac{10}{3} \]

    \[ \frac{5}{2}x = -\frac{3}{4} \] To solve for \( x \): \[ x = \frac{-\frac{3}{4}}{\frac{5}{2}} = -\frac{3}{4} \cdot \frac{2}{5} = -\frac{3}{10} \]

    These equations do not have the same solution.

  3. Pair 3: \[ \frac{x}{3.2} = 1.8 \] To solve for \( x \): \[ x = 1.8 \cdot 3.2 = 5.76 \]

    \[ 1.8x = 3.2 \] To solve for \( x \): \[ x = \frac{3.2}{1.8} = \frac{32}{18} = \frac{16}{9} \approx 1.78 \]

    These equations do not have the same solution.

  4. Pair 4: \[ -3.2x = 0.64 \] To solve for \( x \): \[ x = \frac{0.64}{-3.2} = -0.2 \]

    \[ x \cdot 4 = -0.05 \] To solve for \( x \): \[ x = \frac{-0.05}{4} = -0.0125 \]

    These equations do not have the same solution.

After checking all pairs, it appears that none of the pairs provided have exactly the same solution.

If I can provide any further help or clarifications, please let me know!

You have to find out which equations have the same answer. Like does 3/8x =1 and 1/3x = 1/8 have the same answer

Let's analyze the pairs of equations again to check which pairs have exactly the same solutions.

Pair 1:

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

    Solving for \(x\): \[ x = \frac{1}{\frac{3}{8}} = 1 \cdot \frac{8}{3} = \frac{8}{3} \]

  2. \(\frac{1}{3}x = \frac{1}{8}\)

    Solving for \(x\): \[ x = \frac{1}{\frac{1}{3}} \cdot \frac{1}{8} = 3 \cdot \frac{1}{8} = \frac{3}{8} \]

    Conclusion: These equations do not have the same solution.

Pair 2:

  1. \(-\frac{3}{4}x = \frac{5}{2}\)

    Solving for \(x\): \[ x = \frac{\frac{5}{2}}{-\frac{3}{4}} = \frac{5}{2} \cdot \frac{-4}{3} = -\frac{10}{3} \]

  2. \(\frac{5}{2}x = -\frac{3}{4}\)

    Solving for \(x\): \[ x = \frac{-\frac{3}{4}}{\frac{5}{2}} = -\frac{3}{4} \cdot \frac{2}{5} = -\frac{3}{10} \]

    Conclusion: These equations do not have the same solution.

Pair 3:

  1. \(\frac{x}{3.2} = 1.8\)

    Solving for \(x\): \[ x = 1.8 \cdot 3.2 = 5.76 \]

  2. \(1.8x = 3.2\)

    Solving for \(x\): \[ x = \frac{3.2}{1.8} = \frac{32}{18} = \frac{16}{9} \approx 1.78 \]

    Conclusion: These equations do not have the same solution.

Pair 4:

  1. \(-3.2x = 0.64\)

    Solving for \(x\): \[ x = \frac{0.64}{-3.2} = -0.2 \]

  2. \(x \cdot 4 = -0.05\)

    Solving for \(x\): \[ x = \frac{-0.05}{4} = -0.0125 \]

    Conclusion: These equations do not have the same solution.

After reviewing all pairs of equations, none of the pairs has the same solution. If you have more pairs or further instructions, feel free to share!

Well you have to pick an answer

Apologies for the confusion. Let's carefully evaluate each pair to find out which ones have the same solution.

  1. Pair 1:

    • \( \frac{3}{8}x = 1 \)

      • \( x = \frac{1}{\frac{3}{8}} = \frac{8}{3} \)

    • \( \frac{1}{3}x = \frac{1}{8} \)

      • \( x = \frac{1}{\frac{1}{3}} \cdot \frac{1}{8} = 3 \cdot \frac{1}{8} = \frac{3}{8} \)

    Conclusion: Different solutions.

  2. Pair 2:

    • \( -\frac{3}{4}x = \frac{5}{2} \)

      • \( x = \frac{\frac{5}{2}}{-\frac{3}{4}} = -\frac{10}{3} \)

    • \( \frac{5}{2}x = -\frac{3}{4} \)

      • \( x = \frac{-\frac{3}{4}}{\frac{5}{2}} = -\frac{3}{10} \)

    Conclusion: Different solutions.

  3. Pair 3:

    • \( \frac{x}{3.2} = 1.8 \)

      • \( x = 1.8 \cdot 3.2 = 5.76 \)

    • \( 1.8x = 3.2 \)

      • \( x = \frac{3.2}{1.8} \approx 1.78 \)

    Conclusion: Different solutions.

  4. Pair 4:

    • \( -3.2x = 0.64 \)

      • \( x = \frac{0.64}{-3.2} = -0.2 \)

    • \( x \cdot 4 = -0.05 \)

      • \( x = \frac{-0.05}{4} = -0.0125 \)

    Conclusion: Different solutions.

After reviewing all pairs once again and confirming the calculations:

  • None of the pairs of equations provided have the same solution.

However, if I must choose a pair to check for potential confusion among common pairs, I can say Pair 3 is the one that appears simpler, but still does not yield the same answer ultimately.

If there's anything else I can assist you with, please let me know!

How about pair 4. -3.2x = 0.64 and x/4= -0.05

Let's carefully solve Pair 4:

  1. Equation 1: \[ -3.2x = 0.64 \] To solve for \( x \): \[ x = \frac{0.64}{-3.2} = -0.2 \]

  2. Equation 2: \[ \frac{x}{4} = -0.05 \] To solve for \( x \): \[ x = -0.05 \cdot 4 = -0.2 \]

Conclusion:

Both equations yield the same solution: \[ x = -0.2 \]

Thus, Pair 4: \(-3.2x = 0.64\) and \(\frac{x}{4} = -0.05\) has exactly the same solution.

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