Solved on Dec 08, 2023

Solve the equation $9(x-6)=-27$ in steps, choosing the best reason for each step.

STEP 1

Assumptions
1. The given equation is $9(x-6)=-27$ .
2. Each step in the solution process must be justified with a mathematical reason.

STEP 2

The first step in the solution is the given equation itself.
$9(x-6)=-27$
The reason for this step is that it is the "Given equation".

STEP 3

The next step is to distribute the 9 to both terms inside the parentheses.
$9x - 9 \cdot 6 = -27$
The reason for this step is "Distributive Property", which allows us to multiply the 9 by each term inside the parentheses.

STEP 4

After applying the distributive property, we simplify the multiplication.
$9x - 54 = -27$
The reason for this step is "Simplification", as we have simplified the expression by carrying out the multiplication.

STEP 5

The next step is to add 54 to both sides of the equation to isolate the term with the variable on one side.
$9x - 54 + 54 = -27 + 54$
The reason for this step is "Addition Property of Equality", which states that adding the same number to both sides of an equation will keep the equation balanced.

STEP 6

After adding 54 to both sides, we simplify the equation.
$9x = 27$
The reason for this step is "Simplification", as we have simplified the equation by combining like terms.

STEP 7

The next step is to divide both sides of the equation by 9 to solve for x.
$\frac{9x}{9} = \frac{27}{9}$
The reason for this step is "Division Property of Equality", which states that dividing both sides of an equation by the same nonzero number will keep the equation balanced.

STEP 8

After dividing both sides by 9, we simplify the equation to find the value of x.
$x = 3$
The reason for this step is "Simplification", as we have simplified the equation by carrying out the division.
The solution to the equation $9(x-6)=-27$ is $x=3$ .

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Solve the equation $9(x-6)=-27$ in steps, choosing the best reason for each step.

STEP 1

Assumptions
1. The given equation is $9(x-6)=-27$ .
2. Each step in the solution process must be justified with a mathematical reason.

STEP 2

The first step in the solution is the given equation itself.
$9(x-6)=-27$
The reason for this step is that it is the "Given equation".

STEP 3

The next step is to distribute the 9 to both terms inside the parentheses.
$9x - 9 \cdot 6 = -27$
The reason for this step is "Distributive Property", which allows us to multiply the 9 by each term inside the parentheses.

STEP 4

After applying the distributive property, we simplify the multiplication.
$9x - 54 = -27$
The reason for this step is "Simplification", as we have simplified the expression by carrying out the multiplication.

STEP 5

The next step is to add 54 to both sides of the equation to isolate the term with the variable on one side.
$9x - 54 + 54 = -27 + 54$
The reason for this step is "Addition Property of Equality", which states that adding the same number to both sides of an equation will keep the equation balanced.

STEP 6

After adding 54 to both sides, we simplify the equation.
$9x = 27$
The reason for this step is "Simplification", as we have simplified the equation by combining like terms.

STEP 7

The next step is to divide both sides of the equation by 9 to solve for x.
$\frac{9x}{9} = \frac{27}{9}$
The reason for this step is "Division Property of Equality", which states that dividing both sides of an equation by the same nonzero number will keep the equation balanced.

STEP 8

After dividing both sides by 9, we simplify the equation to find the value of x.
$x = 3$
The reason for this step is "Simplification", as we have simplified the equation by carrying out the division.
The solution to the equation $9(x-6)=-27$ is $x=3$ .

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Solve the equation 9(x−6)=−279(x-6)=-279(x−6)=−27 in steps, choosing the best reason for each step.

STEP 1

Assumptions1. The given equation is 9(x−6)=−279(x-6)=-279(x−6)=−27.2. Each step in the solution process must be justified with a mathematical reason.

STEP 2

The first step in the solution is the given equation itself.9(x−6)=−279(x-6)=-279(x−6)=−27The reason for this step is that it is the "Given equation".

STEP 3

The next step is to distribute the 9 to both terms inside the parentheses.9x−9⋅6=−279x - 9 \cdot 6 = -279x−9⋅6=−27The reason for this step is "Distributive Property", which allows us to multiply the 9 by each term inside the parentheses.

STEP 4

After applying the distributive property, we simplify the multiplication.9x−54=−279x - 54 = -279x−54=−27The reason for this step is "Simplification", as we have simplified the expression by carrying out the multiplication.

STEP 5

STEP 6

After adding 54 to both sides, we simplify the equation.9x=279x = 279x=27The reason for this step is "Simplification", as we have simplified the equation by combining like terms.

STEP 7

The next step is to divide both sides of the equation by 9 to solve for x.9x9=279\frac{9x}{9} = \frac{27}{9}99x​=927​The reason for this step is "Division Property of Equality", which states that dividing both sides of an equation by the same nonzero number will keep the equation balanced.

STEP 8

After dividing both sides by 9, we simplify the equation to find the value of x.x=3x = 3x=3The reason for this step is "Simplification", as we have simplified the equation by carrying out the division.The solution to the equation 9(x−6)=−279(x-6)=-279(x−6)=−27 is x=3x=3x=3.

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

Solve the equation $9(x-6)=-27$ in steps, choosing the best reason for each step.

Assumptions
1. The given equation is $9(x-6)=-27$ .
2. Each step in the solution process must be justified with a mathematical reason.

The first step in the solution is the given equation itself.
$9(x-6)=-27$
The reason for this step is that it is the "Given equation".

The next step is to distribute the 9 to both terms inside the parentheses.
$9x - 9 \cdot 6 = -27$
The reason for this step is "Distributive Property", which allows us to multiply the 9 by each term inside the parentheses.

After applying the distributive property, we simplify the multiplication.
$9x - 54 = -27$
The reason for this step is "Simplification", as we have simplified the expression by carrying out the multiplication.

After adding 54 to both sides, we simplify the equation.
$9x = 27$
The reason for this step is "Simplification", as we have simplified the equation by combining like terms.

The next step is to divide both sides of the equation by 9 to solve for x.
$\frac{9x}{9} = \frac{27}{9}$
The reason for this step is "Division Property of Equality", which states that dividing both sides of an equation by the same nonzero number will keep the equation balanced.

After dividing both sides by 9, we simplify the equation to find the value of x.
$x = 3$
The reason for this step is "Simplification", as we have simplified the equation by carrying out the division.
The solution to the equation $9(x-6)=-27$ is $x=3$ .