Solved on Jan 18, 2024

Solve the linear equation $\frac{x+10}{x}=9$ for $x$ , where $x \neq 0$ .

STEP 1

Assumptions
1. We have the equation $\frac{x+10}{x} = 9$ .
2. $x$ cannot be equal to $0$ .

STEP 2

To solve the equation $\frac{x+10}{x} = 9$ , we need to eliminate the fraction by multiplying both sides of the equation by $x$ .
$x \cdot \frac{x+10}{x} = x \cdot 9$

STEP 3

Simplify the left side of the equation by canceling out $x$ in the numerator and the denominator.
$x+10 = x \cdot 9$

STEP 4

Now, distribute the $x$ on the right side of the equation.
$x+10 = 9x$

STEP 5

To isolate $x$ , we need to get all terms involving $x$ on one side of the equation. Subtract $x$ from both sides.
$x+10 - x = 9x - x$

STEP 6

Simplify both sides of the equation.
$10 = 8x$

STEP 7

To solve for $x$ , divide both sides of the equation by $8$ .
$\frac{10}{8} = \frac{8x}{8}$

STEP 8

Simplify the fraction on the left side and the equation on the right side.
$\frac{5}{4} = x$

STEP 9

We have found the value of $x$ .
$x = \frac{5}{4}$
The solution to the equation $\frac{x+10}{x} = 9$ with the condition $x \neq 0$ is $x = \frac{5}{4}$ .

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Solve the linear equation $\frac{x+10}{x}=9$ for $x$ , where $x \neq 0$ .

STEP 1

Assumptions
1. We have the equation $\frac{x+10}{x} = 9$ .
2. $x$ cannot be equal to $0$ .

STEP 2

To solve the equation $\frac{x+10}{x} = 9$ , we need to eliminate the fraction by multiplying both sides of the equation by $x$ .
$x \cdot \frac{x+10}{x} = x \cdot 9$

STEP 3

Simplify the left side of the equation by canceling out $x$ in the numerator and the denominator.
$x+10 = x \cdot 9$

STEP 4

Now, distribute the $x$ on the right side of the equation.
$x+10 = 9x$

STEP 5

To isolate $x$ , we need to get all terms involving $x$ on one side of the equation. Subtract $x$ from both sides.
$x+10 - x = 9x - x$

STEP 6

Simplify both sides of the equation.
$10 = 8x$

STEP 7

To solve for $x$ , divide both sides of the equation by $8$ .
$\frac{10}{8} = \frac{8x}{8}$

STEP 8

Simplify the fraction on the left side and the equation on the right side.
$\frac{5}{4} = x$

STEP 9

We have found the value of $x$ .
$x = \frac{5}{4}$
The solution to the equation $\frac{x+10}{x} = 9$ with the condition $x \neq 0$ is $x = \frac{5}{4}$ .

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Solve the linear equation x+10x=9\frac{x+10}{x}=9xx+10​=9 for xxx, where x≠0x \neq 0x=0.

STEP 1

Assumptions1. We have the equation x+10x=9\frac{x+10}{x} = 9xx+10​=9.2. xxx cannot be equal to 000.

STEP 2

To solve the equation x+10x=9\frac{x+10}{x} = 9xx+10​=9, we need to eliminate the fraction by multiplying both sides of the equation by xxx.x⋅x+10x=x⋅9x \cdot \frac{x+10}{x} = x \cdot 9x⋅xx+10​=x⋅9

STEP 3

Simplify the left side of the equation by canceling out xxx in the numerator and the denominator.x+10=x⋅9x+10 = x \cdot 9x+10=x⋅9

STEP 4

Now, distribute the xxx on the right side of the equation.x+10=9xx+10 = 9xx+10=9x

STEP 5

To isolate xxx, we need to get all terms involving xxx on one side of the equation. Subtract xxx from both sides.x+10−x=9x−xx+10 - x = 9x - xx+10−x=9x−x

STEP 6

Simplify both sides of the equation.10=8x10 = 8x10=8x

STEP 7

To solve for xxx, divide both sides of the equation by 888.108=8x8\frac{10}{8} = \frac{8x}{8}810​=88x​

STEP 8

Simplify the fraction on the left side and the equation on the right side.54=x\frac{5}{4} = x45​=x

STEP 9

We have found the value of xxx.x=54x = \frac{5}{4}x=45​The solution to the equation x+10x=9\frac{x+10}{x} = 9xx+10​=9 with the condition x≠0x \neq 0x=0 is x=54x = \frac{5}{4}x=45​.

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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 linear equation $\frac{x+10}{x}=9$ for $x$ , where $x \neq 0$ .

Assumptions
1. We have the equation $\frac{x+10}{x} = 9$ .
2. $x$ cannot be equal to $0$ .

To solve the equation $\frac{x+10}{x} = 9$ , we need to eliminate the fraction by multiplying both sides of the equation by $x$ .
$x \cdot \frac{x+10}{x} = x \cdot 9$

Simplify the left side of the equation by canceling out $x$ in the numerator and the denominator.
$x+10 = x \cdot 9$

Now, distribute the $x$ on the right side of the equation.
$x+10 = 9x$

To isolate $x$ , we need to get all terms involving $x$ on one side of the equation. Subtract $x$ from both sides.
$x+10 - x = 9x - x$

Simplify both sides of the equation.
$10 = 8x$

To solve for $x$ , divide both sides of the equation by $8$ .
$\frac{10}{8} = \frac{8x}{8}$

Simplify the fraction on the left side and the equation on the right side.
$\frac{5}{4} = x$

We have found the value of $x$ .
$x = \frac{5}{4}$
The solution to the equation $\frac{x+10}{x} = 9$ with the condition $x \neq 0$ is $x = \frac{5}{4}$ .