QuestionIdentify all equations equivalent to: $-30=14 y$ . Consider properties of equality. Options: $60=-2 \cdot 14 y$ , $-60=14 y \cdot 2$ , $90=14 y \cdot-3$ , $-90=14 y \cdot 3$ .

Studdy Solution

STEP 1

Assumptions1. The given equation is $-30=14y$ . We are looking for equations that are equivalent to the given equation3. The properties of equality state that if you multiply or divide both sides of an equation by the same non-zero number, the equation remains valid

STEP 2

Let's first solve the given equation for $y$ .
$y = \frac{-30}{14}$

STEP 3

Calculate the value of $y$ .
$y = \frac{-30}{14} = -\frac{15}{7}$

STEP 4

Now, let's check the first equation $60=-2 \cdot14y$ . We can rewrite this equation as follows $y = \frac{60}{-2 \cdot14}$

STEP 5

Calculate the value of $y$ for the first equation.
$y = \frac{60}{-2 \cdot14} = -\frac{15}{7}$

STEP 6

Since the value of $y$ for the first equation is equal to the value of $y$ for the given equation, the first equation is equivalent to the given equation.

STEP 7

Now, let's check the second equation $-60=14y \cdot2$ . We can rewrite this equation as follows $y = \frac{-60}{14 \cdot2}$

STEP 8

Calculate the value of $y$ for the second equation.
$y = \frac{-60}{14 \cdot2} = -\frac{15}{7}$

STEP 9

Since the value of $y$ for the second equation is equal to the value of $y$ for the given equation, the second equation is equivalent to the given equation.

STEP 10

Now, let's check the third equation $90=14y \cdot -3$ . We can rewrite this equation as follows $y = \frac{90}{14 \cdot -3}$

STEP 11

Calculate the value of $y$ for the third equation.
$y = \frac{90}{14 \cdot -3} = -\frac{15}{7}$

STEP 12

Since the value of $y$ for the third equation is equal to the value of $y$ for the given equation, the third equation is equivalent to the given equation.

STEP 13

Now, let's check the fourth equation $-90=y \cdot3$ . We can rewrite this equation as follows $y = \frac{-90}{ \cdot3}$

STEP 14

Calculate the value of $y$ for the fourth equation.
$y = \frac{-90}{14 \cdot3} = -\frac{}{7}$

STEP 15

Since the value of $y$ for the fourth equation is equal to the value of $y$ for the given equation, the fourth equation is equivalent to the given equation.
So, all of the given equations are equivalent to the original equation $-30=14y$ .

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QuestionIdentify all equations equivalent to: $-30=14 y$ . Consider properties of equality. Options: $60=-2 \cdot 14 y$ , $-60=14 y \cdot 2$ , $90=14 y \cdot-3$ , $-90=14 y \cdot 3$ .

Studdy Solution

STEP 1

Assumptions1. The given equation is $-30=14y$ . We are looking for equations that are equivalent to the given equation3. The properties of equality state that if you multiply or divide both sides of an equation by the same non-zero number, the equation remains valid

STEP 2

Let's first solve the given equation for $y$ .
$y = \frac{-30}{14}$

STEP 3

Calculate the value of $y$ .
$y = \frac{-30}{14} = -\frac{15}{7}$

STEP 4

Now, let's check the first equation $60=-2 \cdot14y$ . We can rewrite this equation as follows $y = \frac{60}{-2 \cdot14}$

STEP 5

Calculate the value of $y$ for the first equation.
$y = \frac{60}{-2 \cdot14} = -\frac{15}{7}$

STEP 6

Since the value of $y$ for the first equation is equal to the value of $y$ for the given equation, the first equation is equivalent to the given equation.

STEP 7

Now, let's check the second equation $-60=14y \cdot2$ . We can rewrite this equation as follows $y = \frac{-60}{14 \cdot2}$

STEP 8

Calculate the value of $y$ for the second equation.
$y = \frac{-60}{14 \cdot2} = -\frac{15}{7}$

STEP 9

Since the value of $y$ for the second equation is equal to the value of $y$ for the given equation, the second equation is equivalent to the given equation.

STEP 10

Now, let's check the third equation $90=14y \cdot -3$ . We can rewrite this equation as follows $y = \frac{90}{14 \cdot -3}$

STEP 11

Calculate the value of $y$ for the third equation.
$y = \frac{90}{14 \cdot -3} = -\frac{15}{7}$

STEP 12

Since the value of $y$ for the third equation is equal to the value of $y$ for the given equation, the third equation is equivalent to the given equation.

STEP 13

Now, let's check the fourth equation $-90=y \cdot3$ . We can rewrite this equation as follows $y = \frac{-90}{ \cdot3}$

STEP 14

Calculate the value of $y$ for the fourth equation.
$y = \frac{-90}{14 \cdot3} = -\frac{}{7}$

STEP 15

Since the value of $y$ for the fourth equation is equal to the value of $y$ for the given equation, the fourth equation is equivalent to the given equation.
So, all of the given equations are equivalent to the original equation $-30=14y$ .

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QuestionIdentify all equations equivalent to: −30=14y-30=14 y−30=14y. Consider properties of equality. Options: 60=−2⋅14y60=-2 \cdot 14 y60=−2⋅14y, −60=14y⋅2-60=14 y \cdot 2−60=14y⋅2, 90=14y⋅−390=14 y \cdot-390=14y⋅−3, −90=14y⋅3-90=14 y \cdot 3−90=14y⋅3.

Studdy Solution

STEP 1

Assumptions1. The given equation is −30=14y-30=14y−30=14y . We are looking for equations that are equivalent to the given equation3. The properties of equality state that if you multiply or divide both sides of an equation by the same non-zero number, the equation remains valid

STEP 2

Let's first solve the given equation for yyy.y=−3014y = \frac{-30}{14}y=14−30​

STEP 3

Calculate the value of yyy.y=−3014=−157y = \frac{-30}{14} = -\frac{15}{7}y=14−30​=−715​

STEP 4

Now, let's check the first equation 60=−2⋅14y60=-2 \cdot14y60=−2⋅14y. We can rewrite this equation as followsy=60−2⋅14y = \frac{60}{-2 \cdot14}y=−2⋅1460​

STEP 5

Calculate the value of yyy for the first equation.y=60−2⋅14=−157y = \frac{60}{-2 \cdot14} = -\frac{15}{7}y=−2⋅1460​=−715​

STEP 6

Since the value of yyy for the first equation is equal to the value of yyy for the given equation, the first equation is equivalent to the given equation.

STEP 7

Now, let's check the second equation −60=14y⋅2-60=14y \cdot2−60=14y⋅2. We can rewrite this equation as followsy=−6014⋅2y = \frac{-60}{14 \cdot2}y=14⋅2−60​

STEP 8

Calculate the value of yyy for the second equation.y=−6014⋅2=−157y = \frac{-60}{14 \cdot2} = -\frac{15}{7}y=14⋅2−60​=−715​

STEP 9

Since the value of yyy for the second equation is equal to the value of yyy for the given equation, the second equation is equivalent to the given equation.

STEP 10

Now, let's check the third equation 90=14y⋅−390=14y \cdot -390=14y⋅−3. We can rewrite this equation as followsy=9014⋅−3y = \frac{90}{14 \cdot -3}y=14⋅−390​

STEP 11

Calculate the value of yyy for the third equation.y=9014⋅−3=−157y = \frac{90}{14 \cdot -3} = -\frac{15}{7}y=14⋅−390​=−715​

STEP 12

Since the value of yyy for the third equation is equal to the value of yyy for the given equation, the third equation is equivalent to the given equation.

STEP 13

Now, let's check the fourth equation −90=y⋅3-90=y \cdot3−90=y⋅3. We can rewrite this equation as followsy=−90⋅3y = \frac{-90}{ \cdot3}y=⋅3−90​

STEP 14

Calculate the value of yyy for the fourth equation.y=−9014⋅3=−7y = \frac{-90}{14 \cdot3} = -\frac{}{7}y=14⋅3−90​=−7​

STEP 15

Since the value of yyy for the fourth equation is equal to the value of yyy for the given equation, the fourth equation is equivalent to the given equation.So, all of the given equations are equivalent to the original equation −30=14y-30=14y−30=14y.

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QuestionIdentify all equations equivalent to: $-30=14 y$ . Consider properties of equality. Options: $60=-2 \cdot 14 y$ , $-60=14 y \cdot 2$ , $90=14 y \cdot-3$ , $-90=14 y \cdot 3$ .

Assumptions1. The given equation is $-30=14y$ . We are looking for equations that are equivalent to the given equation3. The properties of equality state that if you multiply or divide both sides of an equation by the same non-zero number, the equation remains valid

Let's first solve the given equation for $y$ .
$y = \frac{-30}{14}$

Calculate the value of $y$ .
$y = \frac{-30}{14} = -\frac{15}{7}$

Now, let's check the first equation $60=-2 \cdot14y$ . We can rewrite this equation as follows $y = \frac{60}{-2 \cdot14}$

Calculate the value of $y$ for the first equation.
$y = \frac{60}{-2 \cdot14} = -\frac{15}{7}$

Since the value of $y$ for the first equation is equal to the value of $y$ for the given equation, the first equation is equivalent to the given equation.

Now, let's check the second equation $-60=14y \cdot2$ . We can rewrite this equation as follows $y = \frac{-60}{14 \cdot2}$

Calculate the value of $y$ for the second equation.
$y = \frac{-60}{14 \cdot2} = -\frac{15}{7}$

Since the value of $y$ for the second equation is equal to the value of $y$ for the given equation, the second equation is equivalent to the given equation.

Now, let's check the third equation $90=14y \cdot -3$ . We can rewrite this equation as follows $y = \frac{90}{14 \cdot -3}$

Calculate the value of $y$ for the third equation.
$y = \frac{90}{14 \cdot -3} = -\frac{15}{7}$

Since the value of $y$ for the third equation is equal to the value of $y$ for the given equation, the third equation is equivalent to the given equation.

Now, let's check the fourth equation $-90=y \cdot3$ . We can rewrite this equation as follows $y = \frac{-90}{ \cdot3}$

Calculate the value of $y$ for the fourth equation.
$y = \frac{-90}{14 \cdot3} = -\frac{}{7}$

Since the value of $y$ for the fourth equation is equal to the value of $y$ for the given equation, the fourth equation is equivalent to the given equation.
So, all of the given equations are equivalent to the original equation $-30=14y$ .