Solved on Jan 22, 2024

Solve for $x$ where $-9=\frac{6}{x}$ . Simplify the solution.

STEP 1

Assumptions
1. We are given the equation $-9=\frac{6}{x}$ .
2. We need to solve for the variable $x$ .
3. $x$ cannot be zero, as division by zero is undefined.

STEP 2

To solve for $x$ , we need to isolate it on one side of the equation. We can do this by multiplying both sides of the equation by $x$ to eliminate the fraction.
$x \cdot (-9) = x \cdot \left(\frac{6}{x}\right)$

STEP 3

When we multiply the right side of the equation by $x$ , the $x$ in the numerator and the $x$ in the denominator cancel out, leaving us with:
$-9x = 6$

STEP 4

Now we need to isolate $x$ by dividing both sides of the equation by $-9$ .
$\frac{-9x}{-9} = \frac{6}{-9}$

STEP 5

Simplify both sides of the equation to find the value of $x$ .
$x = -\frac{6}{9}$

STEP 6

We can simplify the fraction $-\frac{6}{9}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 3.
$x = -\frac{6 \div 3}{9 \div 3}$

STEP 7

After simplification, we get the value of $x$ .
$x = -\frac{2}{3}$
The solution for $x$ is $-\frac{2}{3}$ .

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Solve for $x$ where $-9=\frac{6}{x}$ . Simplify the solution.

STEP 1

Assumptions
1. We are given the equation $-9=\frac{6}{x}$ .
2. We need to solve for the variable $x$ .
3. $x$ cannot be zero, as division by zero is undefined.

STEP 2

To solve for $x$ , we need to isolate it on one side of the equation. We can do this by multiplying both sides of the equation by $x$ to eliminate the fraction.
$x \cdot (-9) = x \cdot \left(\frac{6}{x}\right)$

STEP 3

When we multiply the right side of the equation by $x$ , the $x$ in the numerator and the $x$ in the denominator cancel out, leaving us with:
$-9x = 6$

STEP 4

Now we need to isolate $x$ by dividing both sides of the equation by $-9$ .
$\frac{-9x}{-9} = \frac{6}{-9}$

STEP 5

Simplify both sides of the equation to find the value of $x$ .
$x = -\frac{6}{9}$

STEP 6

We can simplify the fraction $-\frac{6}{9}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 3.
$x = -\frac{6 \div 3}{9 \div 3}$

STEP 7

After simplification, we get the value of $x$ .
$x = -\frac{2}{3}$
The solution for $x$ is $-\frac{2}{3}$ .

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Solve for xxx where −9=6x-9=\frac{6}{x}−9=x6​. Simplify the solution.

STEP 1

Assumptions1. We are given the equation −9=6x-9=\frac{6}{x}−9=x6​.2. We need to solve for the variable xxx.3. xxx cannot be zero, as division by zero is undefined.

STEP 2

To solve for xxx, we need to isolate it on one side of the equation. We can do this by multiplying both sides of the equation by xxx to eliminate the fraction.x⋅(−9)=x⋅(6x)x \cdot (-9) = x \cdot \left(\frac{6}{x}\right)x⋅(−9)=x⋅(x6​)

STEP 3

When we multiply the right side of the equation by xxx, the xxx in the numerator and the xxx in the denominator cancel out, leaving us with:−9x=6-9x = 6−9x=6

STEP 4

Now we need to isolate xxx by dividing both sides of the equation by −9-9−9.−9x−9=6−9\frac{-9x}{-9} = \frac{6}{-9}−9−9x​=−96​

STEP 5

Simplify both sides of the equation to find the value of xxx.x=−69x = -\frac{6}{9}x=−96​

STEP 6

We can simplify the fraction −69-\frac{6}{9}−96​ by dividing both the numerator and the denominator by their greatest common divisor, which is 3.x=−6÷39÷3x = -\frac{6 \div 3}{9 \div 3}x=−9÷36÷3​

STEP 7

After simplification, we get the value of xxx.x=−23x = -\frac{2}{3}x=−32​The solution for xxx is −23-\frac{2}{3}−32​.

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Solve for $x$ where $-9=\frac{6}{x}$ . Simplify the solution.

Assumptions
1. We are given the equation $-9=\frac{6}{x}$ .
2. We need to solve for the variable $x$ .
3. $x$ cannot be zero, as division by zero is undefined.

To solve for $x$ , we need to isolate it on one side of the equation. We can do this by multiplying both sides of the equation by $x$ to eliminate the fraction.
$x \cdot (-9) = x \cdot \left(\frac{6}{x}\right)$

When we multiply the right side of the equation by $x$ , the $x$ in the numerator and the $x$ in the denominator cancel out, leaving us with:
$-9x = 6$

Now we need to isolate $x$ by dividing both sides of the equation by $-9$ .
$\frac{-9x}{-9} = \frac{6}{-9}$

Simplify both sides of the equation to find the value of $x$ .
$x = -\frac{6}{9}$

We can simplify the fraction $-\frac{6}{9}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 3.
$x = -\frac{6 \div 3}{9 \div 3}$

After simplification, we get the value of $x$ .
$x = -\frac{2}{3}$
The solution for $x$ is $-\frac{2}{3}$ .