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QuestionIdentify equivalent equations for p−q=−93p-q=-93. Which of these are equivalent?
1. p−q3=−31\frac{p-q}{3}=-31
2. p−q3=−32\frac{p-q}{3}=-32
3. p−q−3=29\frac{p-q}{-3}=29
4. p−q−3=31\frac{p-q}{-3}=31

Studdy Solution

STEP 1

Assumptions1. The given equation is p−q=−93p-q=-93 . We are looking for equivalent equations3. Equivalent equations are equations that have the same solution set4. We can use properties of equality to identify equivalent equations

STEP 2

Let's start with the first equation p−q=−31\frac{p-q}{}=-31. To see if it's equivalent to the given equation, we can multiply both sides by using the multiplication property of equality.
⋅p−q=⋅−31 \cdot \frac{p-q}{} = \cdot -31

STEP 3

implify the left side of the equation by cancelling out the3 in the numerator and the denominator.
p−q=3⋅−31p-q =3 \cdot -31

STEP 4

Calculate the right side of the equation.
p−q=−93p-q = -93This equation is equivalent to the given equation.

STEP 5

Now let's look at the second equation p−q3=−32\frac{p-q}{3}=-32. We can multiply both sides by3 using the multiplication property of equality.
3⋅p−q3=3⋅−323 \cdot \frac{p-q}{3} =3 \cdot -32

STEP 6

implify the left side of the equation by cancelling out the3 in the numerator and the denominator.
p−q=3⋅−32p-q =3 \cdot -32

STEP 7

Calculate the right side of the equation.
p−q=−96p-q = -96This equation is not equivalent to the given equation.

STEP 8

Now let's look at the third equation p−q−3=29\frac{p-q}{-3}=29. We can multiply both sides by -3 using the multiplication property of equality.
−3⋅p−q−3=−3⋅29-3 \cdot \frac{p-q}{-3} = -3 \cdot29

STEP 9

implify the left side of the equation by cancelling out the -3 in the numerator and the denominator.
p−q=−3⋅29p-q = -3 \cdot29

STEP 10

Calculate the right side of the equation.
p−q=−87p-q = -87This equation is not equivalent to the given equation.

STEP 11

Finally, let's look at the fourth equation p−q−3=31\frac{p-q}{-3}=31. We can multiply both sides by -3 using the multiplication property of equality.
−3⋅p−q−3=−3⋅31-3 \cdot \frac{p-q}{-3} = -3 \cdot31

STEP 12

implify the left side of the equation by cancelling out the - in the numerator and the denominator.
p−q=−⋅31p-q = - \cdot31

STEP 13

Calculate the right side of the equation.
p−q=−93p-q = -93This equation is equivalent to the given equation.
So, the equations equivalent to p−q=−93p-q=-93 are p−q3=−31\frac{p-q}{3}=-31 and p−q−3=31\frac{p-q}{-3}=31.

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