QuestionSolve and simplify: $2(3x - 1) = 5 - (x + 3)$ ; find $x =$ .

Studdy Solution

STEP 1

Assumptions1. We are given the equation $(3x -1) =5 - (x +3)$ . We need to solve for $x$

STEP 2

First, we need to distribute the2 on the left side of the equation.
$2(x -1) =6x -2$

STEP 3

Now, distribute the negative sign on the right side of the equation.
$5 - (x +3) =5 - x -3$

STEP 4

implify the right side of the equation.
$- x -3 =2 - x$

STEP 5

Now, we have two simplified equations. Let's put them together.
$x -2 =2 - x$

STEP 6

Next, let's get all the x terms on one side of the equation and the constants on the other side. We can do this by adding x to both sides and adding2 to both sides.
$6x + x =2 +2$

STEP 7

implify both sides of the equation.
$7x =4$

STEP 8

Finally, to solve for x, divide both sides of the equation by7.
$x =4 /7$ So, the solution to the equation is $x =4 /7$ .

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QuestionSolve and simplify: $2(3x - 1) = 5 - (x + 3)$ ; find $x =$ .

Studdy Solution

STEP 1

Assumptions1. We are given the equation $(3x -1) =5 - (x +3)$ . We need to solve for $x$

STEP 2

First, we need to distribute the2 on the left side of the equation.
$2(x -1) =6x -2$

STEP 3

Now, distribute the negative sign on the right side of the equation.
$5 - (x +3) =5 - x -3$

STEP 4

implify the right side of the equation.
$- x -3 =2 - x$

STEP 5

Now, we have two simplified equations. Let's put them together.
$x -2 =2 - x$

STEP 6

Next, let's get all the x terms on one side of the equation and the constants on the other side. We can do this by adding x to both sides and adding2 to both sides.
$6x + x =2 +2$

STEP 7

implify both sides of the equation.
$7x =4$

STEP 8

Finally, to solve for x, divide both sides of the equation by7.
$x =4 /7$ So, the solution to the equation is $x =4 /7$ .

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QuestionSolve and simplify: 2(3x−1)=5−(x+3)2(3x - 1) = 5 - (x + 3)2(3x−1)=5−(x+3); find x=x =x=.

Studdy Solution

STEP 1

Assumptions1. We are given the equation (3x−1)=5−(x+3)(3x -1) =5 - (x +3)(3x−1)=5−(x+3). We need to solve for xxx

STEP 2

First, we need to distribute the2 on the left side of the equation.2(x−1)=6x−22(x -1) =6x -22(x−1)=6x−2

STEP 3

Now, distribute the negative sign on the right side of the equation.5−(x+3)=5−x−35 - (x +3) =5 - x -35−(x+3)=5−x−3

STEP 4

implify the right side of the equation.−x−3=2−x - x -3 =2 - x−x−3=2−x

STEP 5

Now, we have two simplified equations. Let's put them together.x−2=2−xx -2 =2 - xx−2=2−x

STEP 6

Next, let's get all the x terms on one side of the equation and the constants on the other side. We can do this by adding x to both sides and adding2 to both sides.6x+x=2+26x + x =2 +26x+x=2+2

STEP 7

implify both sides of the equation.7x=47x =47x=4

STEP 8

Finally, to solve for x, divide both sides of the equation by7.x=4/7x =4 /7x=4/7So, the solution to the equation is x=4/7x =4 /7x=4/7.

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Studdy solves anything!

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QuestionSolve and simplify: $2(3x - 1) = 5 - (x + 3)$ ; find $x =$ .

Assumptions1. We are given the equation $(3x -1) =5 - (x +3)$ . We need to solve for $x$

First, we need to distribute the2 on the left side of the equation.
$2(x -1) =6x -2$

Now, distribute the negative sign on the right side of the equation.
$5 - (x +3) =5 - x -3$

implify the right side of the equation.
$- x -3 =2 - x$

Now, we have two simplified equations. Let's put them together.
$x -2 =2 - x$

Next, let's get all the x terms on one side of the equation and the constants on the other side. We can do this by adding x to both sides and adding2 to both sides.
$6x + x =2 +2$

implify both sides of the equation.
$7x =4$

Finally, to solve for x, divide both sides of the equation by7.
$x =4 /7$ So, the solution to the equation is $x =4 /7$ .