Question Solve for $x$ in the equation $1 + \frac{6}{5x} = 3$ .

Studdy Solution

STEP 1

Assumptions
1. The given equation is $1 + \frac{6}{5x} = 3$ .
2. We need to solve for $x$ .

STEP 2

To isolate the term containing $x$ , we need to move the constant term on the left side of the equation to the right side.
$1 + \frac{6}{5x} - 1 = 3 - 1$

STEP 3

Perform the subtraction on both sides of the equation.
$\frac{6}{5x} = 2$

STEP 4

To solve for $x$ , we need to isolate $x$ by multiplying both sides of the equation by $5x$ .
$5x \cdot \frac{6}{5x} = 2 \cdot 5x$

STEP 5

On the left side of the equation, the $5x$ in the numerator and denominator cancel each other out, leaving us with $6$ .
$6 = 10x$

STEP 6

Now, divide both sides of the equation by $10$ to solve for $x$ .
$\frac{6}{10} = \frac{10x}{10}$

STEP 7

Simplify both sides of the equation.
$\frac{3}{5} = x$
Therefore, $x = \frac{3}{5}$ .

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Question Solve for $x$ in the equation $1 + \frac{6}{5x} = 3$ .

Studdy Solution

STEP 1

Assumptions
1. The given equation is $1 + \frac{6}{5x} = 3$ .
2. We need to solve for $x$ .

STEP 2

To isolate the term containing $x$ , we need to move the constant term on the left side of the equation to the right side.
$1 + \frac{6}{5x} - 1 = 3 - 1$

STEP 3

Perform the subtraction on both sides of the equation.
$\frac{6}{5x} = 2$

STEP 4

To solve for $x$ , we need to isolate $x$ by multiplying both sides of the equation by $5x$ .
$5x \cdot \frac{6}{5x} = 2 \cdot 5x$

STEP 5

On the left side of the equation, the $5x$ in the numerator and denominator cancel each other out, leaving us with $6$ .
$6 = 10x$

STEP 6

Now, divide both sides of the equation by $10$ to solve for $x$ .
$\frac{6}{10} = \frac{10x}{10}$

STEP 7

Simplify both sides of the equation.
$\frac{3}{5} = x$
Therefore, $x = \frac{3}{5}$ .

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Question Solve for xxx in the equation 1+65x=31 + \frac{6}{5x} = 31+5x6​=3.

Studdy Solution

STEP 1

Assumptions1. The given equation is 1+65x=31 + \frac{6}{5x} = 31+5x6​=3.2. We need to solve for xxx.

STEP 2

To isolate the term containing xxx, we need to move the constant term on the left side of the equation to the right side.1+65x−1=3−11 + \frac{6}{5x} - 1 = 3 - 11+5x6​−1=3−1

STEP 3

Perform the subtraction on both sides of the equation.65x=2\frac{6}{5x} = 25x6​=2

STEP 4

To solve for xxx, we need to isolate xxx by multiplying both sides of the equation by 5x5x5x.5x⋅65x=2⋅5x5x \cdot \frac{6}{5x} = 2 \cdot 5x5x⋅5x6​=2⋅5x

STEP 5

On the left side of the equation, the 5x5x5x in the numerator and denominator cancel each other out, leaving us with 666.6=10x6 = 10x6=10x

STEP 6

Now, divide both sides of the equation by 101010 to solve for xxx.610=10x10\frac{6}{10} = \frac{10x}{10}106​=1010x​

STEP 7

Simplify both sides of the equation.35=x\frac{3}{5} = x53​=xTherefore, x=35x = \frac{3}{5}x=53​.

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Question Solve for $x$ in the equation $1 + \frac{6}{5x} = 3$ .

Assumptions
1. The given equation is $1 + \frac{6}{5x} = 3$ .
2. We need to solve for $x$ .

To isolate the term containing $x$ , we need to move the constant term on the left side of the equation to the right side.
$1 + \frac{6}{5x} - 1 = 3 - 1$

Perform the subtraction on both sides of the equation.
$\frac{6}{5x} = 2$

To solve for $x$ , we need to isolate $x$ by multiplying both sides of the equation by $5x$ .
$5x \cdot \frac{6}{5x} = 2 \cdot 5x$

On the left side of the equation, the $5x$ in the numerator and denominator cancel each other out, leaving us with $6$ .
$6 = 10x$

Now, divide both sides of the equation by $10$ to solve for $x$ .
$\frac{6}{10} = \frac{10x}{10}$

Simplify both sides of the equation.
$\frac{3}{5} = x$
Therefore, $x = \frac{3}{5}$ .