QuestionSolve the equation $-(-8-3 x)=-2(1-x)+6 x$ .

Studdy Solution

STEP 1

Assumptions1. The given equation is $-(-8-3 x)=-(1-x)+6 x$ . We are solving for the variable $x$

STEP 2

First, we need to simplify the equation by distributing the negative sign on the left side of the equation.
$-(-8-x) =8 +x$

STEP 3

Similarly, distribute the negative sign on the right side of the equation.
$-2(1-x) = -2 +2x$

STEP 4

Now, the equation becomes $8 +3x = -2 +2x +6x$

STEP 5

Combine like terms on the right side of the equation.
$8 +3x = -2 +8x$

STEP 6

Rearrange the equation to group the terms with $x$ on one side and the constants on the other side.
$3x -8x = -2 -8$

STEP 7

implify the equation by combining like terms.
$-5x = -10$

STEP 8

Finally, solve for $x$ by dividing both sides of the equation by -5.
$x = -10 / -5$

STEP 9

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

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QuestionSolve the equation $-(-8-3 x)=-2(1-x)+6 x$ .

Studdy Solution

STEP 1

Assumptions1. The given equation is $-(-8-3 x)=-(1-x)+6 x$ . We are solving for the variable $x$

STEP 2

First, we need to simplify the equation by distributing the negative sign on the left side of the equation.
$-(-8-x) =8 +x$

STEP 3

Similarly, distribute the negative sign on the right side of the equation.
$-2(1-x) = -2 +2x$

STEP 4

Now, the equation becomes $8 +3x = -2 +2x +6x$

STEP 5

Combine like terms on the right side of the equation.
$8 +3x = -2 +8x$

STEP 6

Rearrange the equation to group the terms with $x$ on one side and the constants on the other side.
$3x -8x = -2 -8$

STEP 7

implify the equation by combining like terms.
$-5x = -10$

STEP 8

Finally, solve for $x$ by dividing both sides of the equation by -5.
$x = -10 / -5$

STEP 9

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

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QuestionSolve the equation −(−8−3x)=−2(1−x)+6x-(-8-3 x)=-2(1-x)+6 x−(−8−3x)=−2(1−x)+6x.

Studdy Solution

STEP 1

Assumptions1. The given equation is −(−8−3x)=−(1−x)+6x-(-8-3 x)=-(1-x)+6 x−(−8−3x)=−(1−x)+6x . We are solving for the variable xxx

STEP 2

First, we need to simplify the equation by distributing the negative sign on the left side of the equation.−(−8−x)=8+x-(-8-x) =8 +x−(−8−x)=8+x

STEP 3

Similarly, distribute the negative sign on the right side of the equation.−2(1−x)=−2+2x-2(1-x) = -2 +2x−2(1−x)=−2+2x

STEP 4

Now, the equation becomes8+3x=−2+2x+6x8 +3x = -2 +2x +6x8+3x=−2+2x+6x

STEP 5

Combine like terms on the right side of the equation.8+3x=−2+8x8 +3x = -2 +8x8+3x=−2+8x

STEP 6

Rearrange the equation to group the terms with xxx on one side and the constants on the other side.3x−8x=−2−83x -8x = -2 -83x−8x=−2−8

STEP 7

implify the equation by combining like terms.−5x=−10-5x = -10−5x=−10

STEP 8

Finally, solve for xxx by dividing both sides of the equation by -5.x=−10/−5x = -10 / -5x=−10/−5

STEP 9

Calculate the value of xxx.x=2x =2x=2The solution to the equation is x=2x =2x=2.

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QuestionSolve the equation $-(-8-3 x)=-2(1-x)+6 x$ .

Assumptions1. The given equation is $-(-8-3 x)=-(1-x)+6 x$ . We are solving for the variable $x$

First, we need to simplify the equation by distributing the negative sign on the left side of the equation.
$-(-8-x) =8 +x$

Similarly, distribute the negative sign on the right side of the equation.
$-2(1-x) = -2 +2x$

Now, the equation becomes $8 +3x = -2 +2x +6x$

Combine like terms on the right side of the equation.
$8 +3x = -2 +8x$

Rearrange the equation to group the terms with $x$ on one side and the constants on the other side.
$3x -8x = -2 -8$

implify the equation by combining like terms.
$-5x = -10$

Finally, solve for $x$ by dividing both sides of the equation by -5.
$x = -10 / -5$

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