QuestionSolve the equation: $3x - 13 = 7(x + 2) - 4(x - 7)$ .

Studdy Solution

STEP 1

Assumptions1. The equation is $3x -13 =7(x +) -4(x -7)$ . We need to solve for $x$

STEP 2

First, we need to distribute the multiplication in the terms $7(x +2)$ and $-4(x -7)$ .
$7(x +2) =7x +14$ $-4(x -7) = -4x +28$

STEP 3

Substitute the distributed terms back into the equation.
$3x -13 =7x +14 -x +28$

STEP 4

implify the equation by combining like terms on the right side of the equation.
$3x -13 =3x +42$

STEP 5

Subtract $3x$ from both sides of the equation to isolate the variable on one side.
$-13 =42$

STEP 6

This equation is not possible because it states that $-13$ equals $42$ , which is not true. Therefore, there is no solution to this equation.

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QuestionSolve the equation: $3x - 13 = 7(x + 2) - 4(x - 7)$ .

Studdy Solution

STEP 1

Assumptions1. The equation is $3x -13 =7(x +) -4(x -7)$ . We need to solve for $x$

STEP 2

First, we need to distribute the multiplication in the terms $7(x +2)$ and $-4(x -7)$ .
$7(x +2) =7x +14$ $-4(x -7) = -4x +28$

STEP 3

Substitute the distributed terms back into the equation.
$3x -13 =7x +14 -x +28$

STEP 4

implify the equation by combining like terms on the right side of the equation.
$3x -13 =3x +42$

STEP 5

Subtract $3x$ from both sides of the equation to isolate the variable on one side.
$-13 =42$

STEP 6

This equation is not possible because it states that $-13$ equals $42$ , which is not true. Therefore, there is no solution to this equation.

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QuestionSolve the equation: 3x−13=7(x+2)−4(x−7)3x - 13 = 7(x + 2) - 4(x - 7)3x−13=7(x+2)−4(x−7).

Studdy Solution

STEP 1

Assumptions1. The equation is 3x−13=7(x+)−4(x−7)3x -13 =7(x +) -4(x -7)3x−13=7(x+)−4(x−7). We need to solve for xxx

STEP 2

First, we need to distribute the multiplication in the terms 7(x+2)7(x +2)7(x+2) and −4(x−7)-4(x -7)−4(x−7).7(x+2)=7x+147(x +2) =7x +147(x+2)=7x+14−4(x−7)=−4x+28-4(x -7) = -4x +28−4(x−7)=−4x+28

STEP 3

Substitute the distributed terms back into the equation.3x−13=7x+14−x+283x -13 =7x +14 -x +283x−13=7x+14−x+28

STEP 4

implify the equation by combining like terms on the right side of the equation.3x−13=3x+423x -13 =3x +423x−13=3x+42

STEP 5

Subtract 3x3x3x from both sides of the equation to isolate the variable on one side.−13=42-13 =42−13=42

STEP 6

This equation is not possible because it states that −13-13−13 equals 424242, which is not true. Therefore, there is no solution to this equation.

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QuestionSolve the equation: $3x - 13 = 7(x + 2) - 4(x - 7)$ .

Assumptions1. The equation is $3x -13 =7(x +) -4(x -7)$ . We need to solve for $x$

First, we need to distribute the multiplication in the terms $7(x +2)$ and $-4(x -7)$ .
$7(x +2) =7x +14$ $-4(x -7) = -4x +28$

Substitute the distributed terms back into the equation.
$3x -13 =7x +14 -x +28$

implify the equation by combining like terms on the right side of the equation.
$3x -13 =3x +42$

Subtract $3x$ from both sides of the equation to isolate the variable on one side.
$-13 =42$

This equation is not possible because it states that $-13$ equals $42$ , which is not true. Therefore, there is no solution to this equation.