QuestionFind all equations equivalent to $12=4c$ using properties of equality: $2=4c-10$ , $9=4c-2$ , $10=4c-2$ , $4=4c-8$ .

Studdy Solution

STEP 1

Assumptions1. The original equation is $12=4c$ . We are looking for equations that are equivalent to the original equation3. Equivalent equations will have the same solution for $c$ as the original equation

STEP 2

First, we need to solve the original equation for $c$ . We can do this by dividing both sides of the equation by4.
$c = \frac{12}{4}$

STEP 3

Calculate the value of $c$ .
$c = \frac{12}{} =3$

STEP 4

Now that we have the value of $c$ , we can substitute this value into each of the given equations to see if they are equivalent to the original equation.Let's start with the first equation $2=4c-10$
Substitute $c=3$ into the equation $2=4(3)-10$

STEP 5

Calculate the left-hand side of the equation.
$2=12-10$

STEP 6

implify the equation.
$2=2$ This equation is true, so the first equation $2=4c-10$ is equivalent to the original equation.

STEP 7

Now, let's test the second equation $9=4c-2$
Substitute $c=3$ into the equation $9=4(3)-2$

STEP 8

Calculate the left-hand side of the equation.
$=12-2$

STEP 9

implify the equation.
$9=$ This equation is not true, so the second equation $9=4c-2$ is not equivalent to the original equation.

STEP 10

Now, let's test the third equation $10=4c-2$
Substitute $c=3$ into the equation $10=4(3)-2$

STEP 11

Calculate the left-hand side of the equation.
$10=-$

STEP 12

implify the equation.
$10=10$ This equation is true, so the third equation $10=4c-2$ is equivalent to the original equation.

STEP 13

Finally, let's test the fourth equation $=c-8$
Substitute $c=3$ into the equation $=(3)-8$

STEP 14

Calculate the left-hand side of the equation.
$4=12-8$

STEP 15

implify the equation.
$4=4$ This equation is true, so the fourth equation $4=4c-8$ is equivalent to the original equation.
So, the equations equivalent to $12=4c$ are $2=4c-10$ , $10=4c-2$ , and $4=4c-8$ .

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QuestionFind all equations equivalent to $12=4c$ using properties of equality: $2=4c-10$ , $9=4c-2$ , $10=4c-2$ , $4=4c-8$ .

Studdy Solution

STEP 1

Assumptions1. The original equation is $12=4c$ . We are looking for equations that are equivalent to the original equation3. Equivalent equations will have the same solution for $c$ as the original equation

STEP 2

First, we need to solve the original equation for $c$ . We can do this by dividing both sides of the equation by4.
$c = \frac{12}{4}$

STEP 3

Calculate the value of $c$ .
$c = \frac{12}{} =3$

STEP 4

Now that we have the value of $c$ , we can substitute this value into each of the given equations to see if they are equivalent to the original equation.Let's start with the first equation $2=4c-10$
Substitute $c=3$ into the equation $2=4(3)-10$

STEP 5

Calculate the left-hand side of the equation.
$2=12-10$

STEP 6

implify the equation.
$2=2$ This equation is true, so the first equation $2=4c-10$ is equivalent to the original equation.

STEP 7

Now, let's test the second equation $9=4c-2$
Substitute $c=3$ into the equation $9=4(3)-2$

STEP 8

Calculate the left-hand side of the equation.
$=12-2$

STEP 9

implify the equation.
$9=$ This equation is not true, so the second equation $9=4c-2$ is not equivalent to the original equation.

STEP 10

Now, let's test the third equation $10=4c-2$
Substitute $c=3$ into the equation $10=4(3)-2$

STEP 11

Calculate the left-hand side of the equation.
$10=-$

STEP 12

implify the equation.
$10=10$ This equation is true, so the third equation $10=4c-2$ is equivalent to the original equation.

STEP 13

Finally, let's test the fourth equation $=c-8$
Substitute $c=3$ into the equation $=(3)-8$

STEP 14

Calculate the left-hand side of the equation.
$4=12-8$

STEP 15

implify the equation.
$4=4$ This equation is true, so the fourth equation $4=4c-8$ is equivalent to the original equation.
So, the equations equivalent to $12=4c$ are $2=4c-10$ , $10=4c-2$ , and $4=4c-8$ .

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QuestionFind all equations equivalent to 12=4c12=4c12=4c using properties of equality: 2=4c−102=4c-102=4c−10, 9=4c−29=4c-29=4c−2, 10=4c−210=4c-210=4c−2, 4=4c−84=4c-84=4c−8.

Studdy Solution

STEP 1

Assumptions1. The original equation is 12=4c12=4c12=4c . We are looking for equations that are equivalent to the original equation3. Equivalent equations will have the same solution for ccc as the original equation

STEP 2

First, we need to solve the original equation for ccc. We can do this by dividing both sides of the equation by4.c=124c = \frac{12}{4}c=412​

STEP 3

Calculate the value of ccc.c=12=3c = \frac{12}{} =3c=12​=3

STEP 4

Now that we have the value of ccc, we can substitute this value into each of the given equations to see if they are equivalent to the original equation.Let's start with the first equation 2=4c−102=4c-102=4c−10Substitute c=3c=3c=3 into the equation2=4(3)−102=4(3)-102=4(3)−10

STEP 5

Calculate the left-hand side of the equation.2=12−102=12-102=12−10

STEP 6

implify the equation.2=22=22=2This equation is true, so the first equation 2=4c−102=4c-102=4c−10 is equivalent to the original equation.

STEP 7

Now, let's test the second equation 9=4c−29=4c-29=4c−2Substitute c=3c=3c=3 into the equation9=4(3)−29=4(3)-29=4(3)−2

STEP 8

Calculate the left-hand side of the equation.=12−2=12-2=12−2

STEP 9

implify the equation.9=9=9=This equation is not true, so the second equation 9=4c−29=4c-29=4c−2 is not equivalent to the original equation.

STEP 10

Now, let's test the third equation 10=4c−210=4c-210=4c−2Substitute c=3c=3c=3 into the equation10=4(3)−210=4(3)-210=4(3)−2

STEP 11

Calculate the left-hand side of the equation.10=−10=-10=−

STEP 12

implify the equation.10=1010=1010=10This equation is true, so the third equation 10=4c−210=4c-210=4c−2 is equivalent to the original equation.

STEP 13

Finally, let's test the fourth equation =c−8=c-8=c−8Substitute c=3c=3c=3 into the equation=(3)−8=(3)-8=(3)−8

STEP 14

Calculate the left-hand side of the equation.4=12−84=12-84=12−8

STEP 15

implify the equation.4=44=44=4This equation is true, so the fourth equation 4=4c−84=4c-84=4c−8 is equivalent to the original equation.So, the equations equivalent to 12=4c12=4c12=4c are 2=4c−102=4c-102=4c−10, 10=4c−210=4c-210=4c−2, and 4=4c−84=4c-84=4c−8.

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QuestionFind all equations equivalent to $12=4c$ using properties of equality: $2=4c-10$ , $9=4c-2$ , $10=4c-2$ , $4=4c-8$ .

Assumptions1. The original equation is $12=4c$ . We are looking for equations that are equivalent to the original equation3. Equivalent equations will have the same solution for $c$ as the original equation

First, we need to solve the original equation for $c$ . We can do this by dividing both sides of the equation by4.
$c = \frac{12}{4}$

Calculate the value of $c$ .
$c = \frac{12}{} =3$

Now that we have the value of $c$ , we can substitute this value into each of the given equations to see if they are equivalent to the original equation.Let's start with the first equation $2=4c-10$
Substitute $c=3$ into the equation $2=4(3)-10$

Calculate the left-hand side of the equation.
$2=12-10$

implify the equation.
$2=2$ This equation is true, so the first equation $2=4c-10$ is equivalent to the original equation.

Now, let's test the second equation $9=4c-2$
Substitute $c=3$ into the equation $9=4(3)-2$

Calculate the left-hand side of the equation.
$=12-2$

implify the equation.
$9=$ This equation is not true, so the second equation $9=4c-2$ is not equivalent to the original equation.

Now, let's test the third equation $10=4c-2$
Substitute $c=3$ into the equation $10=4(3)-2$

Calculate the left-hand side of the equation.
$10=-$

implify the equation.
$10=10$ This equation is true, so the third equation $10=4c-2$ is equivalent to the original equation.

Finally, let's test the fourth equation $=c-8$
Substitute $c=3$ into the equation $=(3)-8$

Calculate the left-hand side of the equation.
$4=12-8$

implify the equation.
$4=4$ This equation is true, so the fourth equation $4=4c-8$ is equivalent to the original equation.
So, the equations equivalent to $12=4c$ are $2=4c-10$ , $10=4c-2$ , and $4=4c-8$ .