QuestionIs the equation $3 x-7=0$ equivalent to $3 x=-7$ true or false? If false, correct it.

Studdy Solution

STEP 1

Assumptions1. We are given two equations $3x -7 =0$ and $3x = -7$ . We are asked to determine if these two equations are equivalent

STEP 2

Let's first solve the first equation for $x$ .
$x -7 =0$
To isolate $x$ , we need to add7 to both sides of the equation.
$x =7$

STEP 3

Now, divide both sides of the equation by3 to solve for $x$ .
$x =7/3$

STEP 4

Now, let's solve the second equation for $x$ .
$3x = -7$
To solve for $x$ , divide both sides of the equation by3.
$x = -7/3$

STEP 5

Now that we have solved both equations, we can compare the solutions.The solution to the first equation is $x =7/3$ and the solution to the second equation is $x = -7/3$ .
Since these solutions are not the same, the two equations are not equivalent.Therefore, the statement "The equation $3x -7 =0$ is equivalent to $3x = -7$ " is false.

STEP 6

To make the statement true, we can change the second equation to match the first equation.The correct statement would be "The equation $3x - =0$ is equivalent to $3x =$ "

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QuestionIs the equation $3 x-7=0$ equivalent to $3 x=-7$ true or false? If false, correct it.

Studdy Solution

STEP 1

Assumptions1. We are given two equations $3x -7 =0$ and $3x = -7$ . We are asked to determine if these two equations are equivalent

STEP 2

Let's first solve the first equation for $x$ .
$x -7 =0$
To isolate $x$ , we need to add7 to both sides of the equation.
$x =7$

STEP 3

Now, divide both sides of the equation by3 to solve for $x$ .
$x =7/3$

STEP 4

Now, let's solve the second equation for $x$ .
$3x = -7$
To solve for $x$ , divide both sides of the equation by3.
$x = -7/3$

STEP 5

STEP 6

To make the statement true, we can change the second equation to match the first equation.The correct statement would be "The equation $3x - =0$ is equivalent to $3x =$ "

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QuestionIs the equation 3x−7=03 x-7=03x−7=0 equivalent to 3x=−73 x=-73x=−7 true or false? If false, correct it.

Studdy Solution

STEP 1

Assumptions1. We are given two equations 3x−7=03x -7 =03x−7=0 and 3x=−73x = -73x=−7 . We are asked to determine if these two equations are equivalent

STEP 2

Let's first solve the first equation for xxx.x−7=0x -7 =0x−7=0To isolate xxx, we need to add7 to both sides of the equation.x=7x =7x=7

STEP 3

Now, divide both sides of the equation by3 to solve for xxx.x=7/3x =7/3x=7/3

STEP 4

Now, let's solve the second equation for xxx.3x=−73x = -73x=−7To solve for xxx, divide both sides of the equation by3.x=−7/3x = -7/3x=−7/3

STEP 5

STEP 6

To make the statement true, we can change the second equation to match the first equation.The correct statement would be "The equation 3x−=03x - =03x−=0 is equivalent to 3x=3x =3x="

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QuestionIs the equation $3 x-7=0$ equivalent to $3 x=-7$ true or false? If false, correct it.

Assumptions1. We are given two equations $3x -7 =0$ and $3x = -7$ . We are asked to determine if these two equations are equivalent

Let's first solve the first equation for $x$ .
$x -7 =0$
To isolate $x$ , we need to add7 to both sides of the equation.
$x =7$

Now, divide both sides of the equation by3 to solve for $x$ .
$x =7/3$

Now, let's solve the second equation for $x$ .
$3x = -7$
To solve for $x$ , divide both sides of the equation by3.
$x = -7/3$

To make the statement true, we can change the second equation to match the first equation.The correct statement would be "The equation $3x - =0$ is equivalent to $3x =$ "