QuestionSolve the equation: $6(2 x-6)=-7(-2 x+4)$ .

Studdy Solution

STEP 1

Assumptions1. We are given the equation $6( x-6)=-7(- x+4)$ . We are solving for $x$

STEP 2

First, we need to distribute the $6$ on the left side of the equation and the $-7$ on the right side of the equation.
$6(2 x-6) =12x -36$ $-7(-2 x+4) =14x -28$

STEP 3

Now, we substitute these results back into the equation.
$12x -36 =14x -28$

STEP 4

Next, we want to isolate $x$ on one side of the equation. We can do this by subtracting $12x$ from both sides of the equation.
$-36 =2x -28$

STEP 5

Now, we want to isolate $x$ even further by adding $28$ to both sides of the equation.
$-8 =2x$

STEP 6

Finally, we divide both sides of the equation by $2$ to solve for $x$ .
$x = -8 /2$

STEP 7

Calculate the value of $x$ .
$x = - /2 = -4$ The solution to the equation is $x = -4$ .

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QuestionSolve the equation: $6(2 x-6)=-7(-2 x+4)$ .

Studdy Solution

STEP 1

Assumptions1. We are given the equation $6( x-6)=-7(- x+4)$ . We are solving for $x$

STEP 2

First, we need to distribute the $6$ on the left side of the equation and the $-7$ on the right side of the equation.
$6(2 x-6) =12x -36$ $-7(-2 x+4) =14x -28$

STEP 3

Now, we substitute these results back into the equation.
$12x -36 =14x -28$

STEP 4

Next, we want to isolate $x$ on one side of the equation. We can do this by subtracting $12x$ from both sides of the equation.
$-36 =2x -28$

STEP 5

Now, we want to isolate $x$ even further by adding $28$ to both sides of the equation.
$-8 =2x$

STEP 6

Finally, we divide both sides of the equation by $2$ to solve for $x$ .
$x = -8 /2$

STEP 7

Calculate the value of $x$ .
$x = - /2 = -4$ The solution to the equation is $x = -4$ .

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QuestionSolve the equation: 6(2x−6)=−7(−2x+4)6(2 x-6)=-7(-2 x+4)6(2x−6)=−7(−2x+4).

Studdy Solution

STEP 1

Assumptions1. We are given the equation 6(x−6)=−7(−x+4)6( x-6)=-7(- x+4)6(x−6)=−7(−x+4). We are solving for xxx

STEP 2

First, we need to distribute the 666 on the left side of the equation and the −7-7−7 on the right side of the equation.6(2x−6)=12x−366(2 x-6) =12x -366(2x−6)=12x−36−7(−2x+4)=14x−28-7(-2 x+4) =14x -28−7(−2x+4)=14x−28

STEP 3

Now, we substitute these results back into the equation.12x−36=14x−2812x -36 =14x -2812x−36=14x−28

STEP 4

Next, we want to isolate xxx on one side of the equation. We can do this by subtracting 12x12x12x from both sides of the equation.−36=2x−28-36 =2x -28−36=2x−28

STEP 5

Now, we want to isolate xxx even further by adding 282828 to both sides of the equation.−8=2x-8 =2x−8=2x

STEP 6

Finally, we divide both sides of the equation by 222 to solve for xxx.x=−8/2x = -8 /2x=−8/2

STEP 7

Calculate the value of xxx.x=−/2=−4x = - /2 = -4x=−/2=−4The solution to the equation is x=−4x = -4x=−4.

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QuestionSolve the equation: $6(2 x-6)=-7(-2 x+4)$ .

Assumptions1. We are given the equation $6( x-6)=-7(- x+4)$ . We are solving for $x$

First, we need to distribute the $6$ on the left side of the equation and the $-7$ on the right side of the equation.
$6(2 x-6) =12x -36$ $-7(-2 x+4) =14x -28$

Now, we substitute these results back into the equation.
$12x -36 =14x -28$

Next, we want to isolate $x$ on one side of the equation. We can do this by subtracting $12x$ from both sides of the equation.
$-36 =2x -28$

Now, we want to isolate $x$ even further by adding $28$ to both sides of the equation.
$-8 =2x$

Finally, we divide both sides of the equation by $2$ to solve for $x$ .
$x = -8 /2$

Calculate the value of $x$ .
$x = - /2 = -4$ The solution to the equation is $x = -4$ .