QuestionSolve the equation: $3 x - (x + 9) = 4 x + 15 + 2(x - 8)$ .

Studdy Solution

STEP 1

Assumptions1. The given equation is $3x - (x +9) =4x +15 +(x -8)$ . We are solving for the variable $x$

STEP 2

First, we need to simplify the equation by distributing the negative sign on the left-hand side of the equation.
$x - x -9 =4x +15 +2(x -8)$

STEP 3

Next, simplify the equation by distributing the2 on the right-hand side of the equation.
$3x - x -9 =x +15 +2x -16$

STEP 4

Now, combine like terms on both sides of the equation.
$2x -9 =6x -1$

STEP 5

Next, we need to isolate $x$ by subtracting $2x$ from both sides of the equation.
$-9 =4x -1$

STEP 6

Then, add1 to both sides of the equation to further isolate $x$ .
$-8 =4x$

STEP 7

Finally, divide both sides of the equation by4 to solve for $x$ .
$-2 = x$ So, the solution to the equation is $x = -2$ .

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QuestionSolve the equation: $3 x - (x + 9) = 4 x + 15 + 2(x - 8)$ .

Studdy Solution

STEP 1

Assumptions1. The given equation is $3x - (x +9) =4x +15 +(x -8)$ . We are solving for the variable $x$

STEP 2

First, we need to simplify the equation by distributing the negative sign on the left-hand side of the equation.
$x - x -9 =4x +15 +2(x -8)$

STEP 3

Next, simplify the equation by distributing the2 on the right-hand side of the equation.
$3x - x -9 =x +15 +2x -16$

STEP 4

Now, combine like terms on both sides of the equation.
$2x -9 =6x -1$

STEP 5

Next, we need to isolate $x$ by subtracting $2x$ from both sides of the equation.
$-9 =4x -1$

STEP 6

Then, add1 to both sides of the equation to further isolate $x$ .
$-8 =4x$

STEP 7

Finally, divide both sides of the equation by4 to solve for $x$ .
$-2 = x$ So, the solution to the equation is $x = -2$ .

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QuestionSolve the equation: 3x−(x+9)=4x+15+2(x−8)3 x - (x + 9) = 4 x + 15 + 2(x - 8)3x−(x+9)=4x+15+2(x−8).

Studdy Solution

STEP 1

Assumptions1. The given equation is 3x−(x+9)=4x+15+(x−8)3x - (x +9) =4x +15 +(x -8)3x−(x+9)=4x+15+(x−8). We are solving for the variable xxx

STEP 2

First, we need to simplify the equation by distributing the negative sign on the left-hand side of the equation.x−x−9=4x+15+2(x−8)x - x -9 =4x +15 +2(x -8)x−x−9=4x+15+2(x−8)

STEP 3

Next, simplify the equation by distributing the2 on the right-hand side of the equation.3x−x−9=x+15+2x−163x - x -9 =x +15 +2x -163x−x−9=x+15+2x−16

STEP 4

Now, combine like terms on both sides of the equation.2x−9=6x−12x -9 =6x -12x−9=6x−1

STEP 5

Next, we need to isolate xxx by subtracting 2x2x2x from both sides of the equation.−9=4x−1-9 =4x -1−9=4x−1

STEP 6

Then, add1 to both sides of the equation to further isolate xxx.−8=4x-8 =4x−8=4x

STEP 7

Finally, divide both sides of the equation by4 to solve for xxx.−2=x-2 = x−2=xSo, the solution to the equation is x=−2x = -2x=−2.

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QuestionSolve the equation: $3 x - (x + 9) = 4 x + 15 + 2(x - 8)$ .

Assumptions1. The given equation is $3x - (x +9) =4x +15 +(x -8)$ . We are solving for the variable $x$

First, we need to simplify the equation by distributing the negative sign on the left-hand side of the equation.
$x - x -9 =4x +15 +2(x -8)$

Next, simplify the equation by distributing the2 on the right-hand side of the equation.
$3x - x -9 =x +15 +2x -16$

Now, combine like terms on both sides of the equation.
$2x -9 =6x -1$

Next, we need to isolate $x$ by subtracting $2x$ from both sides of the equation.
$-9 =4x -1$

Then, add1 to both sides of the equation to further isolate $x$ .
$-8 =4x$

Finally, divide both sides of the equation by4 to solve for $x$ .
$-2 = x$ So, the solution to the equation is $x = -2$ .