Question Find the value of $x$ that makes the statement $\frac{x-4}{2x} = \frac{1}{3}$ true.

Studdy Solution

STEP 1

Assumptions
1. The problem is asking to find the value of $x$ that makes the ratio $x-4: 2x$ equivalent to $1:3$ .

STEP 2

A ratio is equivalent to a fraction. We can set up the equation as follows:
$\frac{x-4}{2x} = \frac{1}{3}$

STEP 3

To solve for $x$ , we can cross-multiply. This means multiplying the numerator of the first fraction by the denominator of the second fraction, and setting it equal to the product of the denominator of the first fraction and the numerator of the second fraction.
$(x-4) \cdot 3 = 1 \cdot 2x$

STEP 4

Simplify both sides of the equation.
$3x - 12 = 2x$

STEP 5

Subtract $2x$ from both sides of the equation to isolate $x$ on one side.
$3x - 2x = 12$

STEP 6

Simplify to find the value of $x$ .
$x = 12$
So, the value of $x$ that makes the statement $x-4: 2x$ equivalent to $1: 3$ is $x = 12$ .

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Question Find the value of $x$ that makes the statement $\frac{x-4}{2x} = \frac{1}{3}$ true.

Studdy Solution

STEP 1

Assumptions
1. The problem is asking to find the value of $x$ that makes the ratio $x-4: 2x$ equivalent to $1:3$ .

STEP 2

A ratio is equivalent to a fraction. We can set up the equation as follows:
$\frac{x-4}{2x} = \frac{1}{3}$

STEP 3

To solve for $x$ , we can cross-multiply. This means multiplying the numerator of the first fraction by the denominator of the second fraction, and setting it equal to the product of the denominator of the first fraction and the numerator of the second fraction.
$(x-4) \cdot 3 = 1 \cdot 2x$

STEP 4

Simplify both sides of the equation.
$3x - 12 = 2x$

STEP 5

Subtract $2x$ from both sides of the equation to isolate $x$ on one side.
$3x - 2x = 12$

STEP 6

Simplify to find the value of $x$ .
$x = 12$
So, the value of $x$ that makes the statement $x-4: 2x$ equivalent to $1: 3$ is $x = 12$ .

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Question Find the value of xxx that makes the statement x−42x=13\frac{x-4}{2x} = \frac{1}{3}2xx−4​=31​ true.

Studdy Solution

STEP 1

Assumptions1. The problem is asking to find the value of xxx that makes the ratio x−4:2xx-4: 2xx−4:2x equivalent to 1:31:31:3.

STEP 2

A ratio is equivalent to a fraction. We can set up the equation as follows:x−42x=13\frac{x-4}{2x} = \frac{1}{3}2xx−4​=31​

STEP 3

STEP 4

Simplify both sides of the equation.3x−12=2x3x - 12 = 2x3x−12=2x

STEP 5

Subtract 2x2x2x from both sides of the equation to isolate xxx on one side.3x−2x=123x - 2x = 123x−2x=12

STEP 6

Simplify to find the value of xxx.x=12x = 12x=12So, the value of xxx that makes the statement x−4:2xx-4: 2xx−4:2x equivalent to 1:31: 31:3 is x=12x = 12x=12.

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Question Find the value of $x$ that makes the statement $\frac{x-4}{2x} = \frac{1}{3}$ true.

Assumptions
1. The problem is asking to find the value of $x$ that makes the ratio $x-4: 2x$ equivalent to $1:3$ .

A ratio is equivalent to a fraction. We can set up the equation as follows:
$\frac{x-4}{2x} = \frac{1}{3}$

Simplify both sides of the equation.
$3x - 12 = 2x$

Subtract $2x$ from both sides of the equation to isolate $x$ on one side.
$3x - 2x = 12$

Simplify to find the value of $x$ .
$x = 12$
So, the value of $x$ that makes the statement $x-4: 2x$ equivalent to $1: 3$ is $x = 12$ .