Solved on Jan 18, 2024

Find the value of $x$ that satisfies the equation $2(x-3)=9-x$ .

STEP 1

Assumptions
1. We are given the equation $2(x-3)=9-x$ .
2. We need to solve for the variable $x$ .

STEP 2

First, we will distribute the $2$ on the left side of the equation to both terms inside the parentheses.
$2(x-3) = 2 \cdot x + 2 \cdot (-3)$

STEP 3

Perform the multiplication to simplify the left side of the equation.
$2x - 6 = 9 - x$

STEP 4

Next, we want to 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 of the equation to move the $-x$ from the right to the left side.
$2x - 6 + x = 9 - x + x$

STEP 5

Combine like terms on both sides of the equation.
$3x - 6 = 9$

STEP 6

Now, we will add $6$ to both sides of the equation to isolate the term with $x$ on one side.
$3x - 6 + 6 = 9 + 6$

STEP 7

Simplify both sides of the equation.
$3x = 15$

STEP 8

To solve for $x$ , divide both sides of the equation by $3$ .
$\frac{3x}{3} = \frac{15}{3}$

STEP 9

Calculate the value of $x$ .
$x = 5$
The solution to the equation $2(x-3)=9-x$ is $x = 5$ .

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Find the value of $x$ that satisfies the equation $2(x-3)=9-x$ .

STEP 1

Assumptions
1. We are given the equation $2(x-3)=9-x$ .
2. We need to solve for the variable $x$ .

STEP 2

First, we will distribute the $2$ on the left side of the equation to both terms inside the parentheses.
$2(x-3) = 2 \cdot x + 2 \cdot (-3)$

STEP 3

Perform the multiplication to simplify the left side of the equation.
$2x - 6 = 9 - x$

STEP 4

Next, we want to 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 of the equation to move the $-x$ from the right to the left side.
$2x - 6 + x = 9 - x + x$

STEP 5

Combine like terms on both sides of the equation.
$3x - 6 = 9$

STEP 6

Now, we will add $6$ to both sides of the equation to isolate the term with $x$ on one side.
$3x - 6 + 6 = 9 + 6$

STEP 7

Simplify both sides of the equation.
$3x = 15$

STEP 8

To solve for $x$ , divide both sides of the equation by $3$ .
$\frac{3x}{3} = \frac{15}{3}$

STEP 9

Calculate the value of $x$ .
$x = 5$
The solution to the equation $2(x-3)=9-x$ is $x = 5$ .

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Find the value of xxx that satisfies the equation 2(x−3)=9−x2(x-3)=9-x2(x−3)=9−x.

STEP 1

Assumptions1. We are given the equation 2(x−3)=9−x2(x-3)=9-x2(x−3)=9−x.2. We need to solve for the variable xxx.

STEP 2

First, we will distribute the 222 on the left side of the equation to both terms inside the parentheses.2(x−3)=2⋅x+2⋅(−3)2(x-3) = 2 \cdot x + 2 \cdot (-3)2(x−3)=2⋅x+2⋅(−3)

STEP 3

Perform the multiplication to simplify the left side of the equation.2x−6=9−x2x - 6 = 9 - x2x−6=9−x

STEP 4

Next, we want to get all the xxx terms on one side of the equation and the constants on the other side. We can do this by adding xxx to both sides of the equation to move the −x-x−x from the right to the left side.2x−6+x=9−x+x2x - 6 + x = 9 - x + x2x−6+x=9−x+x

STEP 5

Combine like terms on both sides of the equation.3x−6=93x - 6 = 93x−6=9

STEP 6

Now, we will add 666 to both sides of the equation to isolate the term with xxx on one side.3x−6+6=9+63x - 6 + 6 = 9 + 63x−6+6=9+6

STEP 7

Simplify both sides of the equation.3x=153x = 153x=15

STEP 8

To solve for xxx, divide both sides of the equation by 333.3x3=153\frac{3x}{3} = \frac{15}{3}33x​=315​

STEP 9

Calculate the value of xxx.x=5x = 5x=5The solution to the equation 2(x−3)=9−x2(x-3)=9-x2(x−3)=9−x is x=5x = 5x=5.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the value of $x$ that satisfies the equation $2(x-3)=9-x$ .

Assumptions
1. We are given the equation $2(x-3)=9-x$ .
2. We need to solve for the variable $x$ .

First, we will distribute the $2$ on the left side of the equation to both terms inside the parentheses.
$2(x-3) = 2 \cdot x + 2 \cdot (-3)$

Perform the multiplication to simplify the left side of the equation.
$2x - 6 = 9 - x$

Next, we want to 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 of the equation to move the $-x$ from the right to the left side.
$2x - 6 + x = 9 - x + x$

Combine like terms on both sides of the equation.
$3x - 6 = 9$

Now, we will add $6$ to both sides of the equation to isolate the term with $x$ on one side.
$3x - 6 + 6 = 9 + 6$

Simplify both sides of the equation.
$3x = 15$

To solve for $x$ , divide both sides of the equation by $3$ .
$\frac{3x}{3} = \frac{15}{3}$

Calculate the value of $x$ .
$x = 5$
The solution to the equation $2(x-3)=9-x$ is $x = 5$ .