QuestionSelect all equations equivalent to $9=10 s$ : $6=10 s-2$ , $7=10 s-2$ , $4=10 s-5$ , $8=10 s-3$ .

Studdy Solution

STEP 1

Assumptions1. The original equation is $9=10s$ . The properties of equality state that a. If the same number is added to both sides of an equation, the equation remains true. b. If the same number is subtracted from both sides of an equation, the equation remains true. c. If both sides of an equation are multiplied by the same number, the equation remains true. d. If both sides of an equation are divided by the same non-zero number, the equation remains true.

STEP 2

We will use the properties of equality to transform the original equation into the form of each of the given equations.Let's start with the first equation $6=10s-2$ .To transform the original equation into the form of the first equation, we need to subtract the same number from both sides of the original equation. $9-=10s-$

STEP 3

Calculate the left side of the equation.
$9-3=6$ So, the transformed equation is $6=10s-3$ , which is not equivalent to the first equation $6=10s-2$ .

STEP 4

Now, let's transform the original equation into the form of the second equation $7=10s-2$ .
To do this, we need to subtract the same number from both sides of the original equation.
$9-2=10s-2$

STEP 5

Calculate the left side of the equation.
$9-2=7$ So, the transformed equation is $7=10s-2$ , which is equivalent to the second equation $7=10s-2$ .

STEP 6

Next, let's transform the original equation into the form of the third equation $4=10s-5$ .
To do this, we need to subtract the same number from both sides of the original equation.
$9-5=10s-5$

STEP 7

Calculate the left side of the equation.
$9-5=4$ So, the transformed equation is $4=10s-5$ , which is equivalent to the third equation $4=10s-5$ .

STEP 8

Finally, let's transform the original equation into the form of the fourth equation $8=10s-3$ .
To do this, we need to subtract the same number from both sides of the original equation.
$-1=10s-1$

STEP 9

Calculate the left side of the equation.
$9-=8$ So, the transformed equation is $8=s-$ , which is not equivalent to the fourth equation $8=s-3$ .
The equivalent equations to the original equation $9=s$ are $7=s-2$ and $4=s-5$ .

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QuestionSelect all equations equivalent to $9=10 s$ : $6=10 s-2$ , $7=10 s-2$ , $4=10 s-5$ , $8=10 s-3$ .

Studdy Solution

STEP 1

STEP 2

STEP 3

Calculate the left side of the equation.
$9-3=6$ So, the transformed equation is $6=10s-3$ , which is not equivalent to the first equation $6=10s-2$ .

STEP 4

Now, let's transform the original equation into the form of the second equation $7=10s-2$ .
To do this, we need to subtract the same number from both sides of the original equation.
$9-2=10s-2$

STEP 5

Calculate the left side of the equation.
$9-2=7$ So, the transformed equation is $7=10s-2$ , which is equivalent to the second equation $7=10s-2$ .

STEP 6

Next, let's transform the original equation into the form of the third equation $4=10s-5$ .
To do this, we need to subtract the same number from both sides of the original equation.
$9-5=10s-5$

STEP 7

Calculate the left side of the equation.
$9-5=4$ So, the transformed equation is $4=10s-5$ , which is equivalent to the third equation $4=10s-5$ .

STEP 8

Finally, let's transform the original equation into the form of the fourth equation $8=10s-3$ .
To do this, we need to subtract the same number from both sides of the original equation.
$-1=10s-1$

STEP 9

Calculate the left side of the equation.
$9-=8$ So, the transformed equation is $8=s-$ , which is not equivalent to the fourth equation $8=s-3$ .
The equivalent equations to the original equation $9=s$ are $7=s-2$ and $4=s-5$ .

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QuestionSelect all equations equivalent to 9=10s9=10 s9=10s: 6=10s−26=10 s-26=10s−2, 7=10s−27=10 s-27=10s−2, 4=10s−54=10 s-54=10s−5, 8=10s−38=10 s-38=10s−3.

Studdy Solution

STEP 1

STEP 2

STEP 3

Calculate the left side of the equation.9−3=69-3=69−3=6So, the transformed equation is 6=10s−36=10s-36=10s−3, which is not equivalent to the first equation 6=10s−26=10s-26=10s−2.

STEP 4

Now, let's transform the original equation into the form of the second equation 7=10s−27=10s-27=10s−2.To do this, we need to subtract the same number from both sides of the original equation.9−2=10s−29-2=10s-29−2=10s−2

STEP 5

Calculate the left side of the equation.9−2=79-2=79−2=7So, the transformed equation is 7=10s−27=10s-27=10s−2, which is equivalent to the second equation 7=10s−27=10s-27=10s−2.

STEP 6

Next, let's transform the original equation into the form of the third equation 4=10s−54=10s-54=10s−5.To do this, we need to subtract the same number from both sides of the original equation.9−5=10s−59-5=10s-59−5=10s−5

STEP 7

Calculate the left side of the equation.9−5=49-5=49−5=4So, the transformed equation is 4=10s−54=10s-54=10s−5, which is equivalent to the third equation 4=10s−54=10s-54=10s−5.

STEP 8

Finally, let's transform the original equation into the form of the fourth equation 8=10s−38=10s-38=10s−3.To do this, we need to subtract the same number from both sides of the original equation.−1=10s−1-1=10s-1−1=10s−1

STEP 9

Calculate the left side of the equation.9−=89-=89−=8So, the transformed equation is 8=s−8=s-8=s−, which is not equivalent to the fourth equation 8=s−38=s-38=s−3.The equivalent equations to the original equation 9=s9=s9=s are 7=s−27=s-27=s−2 and 4=s−54=s-54=s−5.

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QuestionSelect all equations equivalent to $9=10 s$ : $6=10 s-2$ , $7=10 s-2$ , $4=10 s-5$ , $8=10 s-3$ .

Calculate the left side of the equation.
$9-3=6$ So, the transformed equation is $6=10s-3$ , which is not equivalent to the first equation $6=10s-2$ .

Now, let's transform the original equation into the form of the second equation $7=10s-2$ .
To do this, we need to subtract the same number from both sides of the original equation.
$9-2=10s-2$

Calculate the left side of the equation.
$9-2=7$ So, the transformed equation is $7=10s-2$ , which is equivalent to the second equation $7=10s-2$ .

Next, let's transform the original equation into the form of the third equation $4=10s-5$ .
To do this, we need to subtract the same number from both sides of the original equation.
$9-5=10s-5$

Calculate the left side of the equation.
$9-5=4$ So, the transformed equation is $4=10s-5$ , which is equivalent to the third equation $4=10s-5$ .

Finally, let's transform the original equation into the form of the fourth equation $8=10s-3$ .
To do this, we need to subtract the same number from both sides of the original equation.
$-1=10s-1$

Calculate the left side of the equation.
$9-=8$ So, the transformed equation is $8=s-$ , which is not equivalent to the fourth equation $8=s-3$ .
The equivalent equations to the original equation $9=s$ are $7=s-2$ and $4=s-5$ .