QuestionSolve the proportion using cross products: $\frac{3}{4}=\frac{9}{x-7}$ . Find $x$ .

Studdy Solution

STEP 1

Assumptions1. The given proportion is $\frac{3}{4}=\frac{9}{x-7}$ . . We are asked to solve for $x$ .
3. The cross products of a proportion are equal.

STEP 2

We start by setting up the cross products of the proportion. The cross products of a proportion $\frac{a}{b}=\frac{c}{d}$ are $a \cdot d$ and $b \cdot c$ .
$\cdot (x-7) =4 \cdot9$

STEP 3

Now, simplify the right side of the equation.
$3 \cdot (x-7) =36$

STEP 4

istribute the3 on the left side of the equation.
$3x -21 =36$

STEP 5

Add21 to both sides of the equation to isolate the term with $x$ on one side.
$3x =36 +21$

STEP 6

implify the right side of the equation.
$3x =57$

STEP 7

Finally, divide both sides of the equation by3 to solve for $x$ .
$x = \frac{57}{3}$

STEP 8

implify the right side of the equation to get the final solution.
$x =19$ So, the solution to the proportion is $x =19$ .

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QuestionSolve the proportion using cross products: $\frac{3}{4}=\frac{9}{x-7}$ . Find $x$ .

Studdy Solution

STEP 1

Assumptions1. The given proportion is $\frac{3}{4}=\frac{9}{x-7}$ . . We are asked to solve for $x$ .
3. The cross products of a proportion are equal.

STEP 2

We start by setting up the cross products of the proportion. The cross products of a proportion $\frac{a}{b}=\frac{c}{d}$ are $a \cdot d$ and $b \cdot c$ .
$\cdot (x-7) =4 \cdot9$

STEP 3

Now, simplify the right side of the equation.
$3 \cdot (x-7) =36$

STEP 4

istribute the3 on the left side of the equation.
$3x -21 =36$

STEP 5

Add21 to both sides of the equation to isolate the term with $x$ on one side.
$3x =36 +21$

STEP 6

implify the right side of the equation.
$3x =57$

STEP 7

Finally, divide both sides of the equation by3 to solve for $x$ .
$x = \frac{57}{3}$

STEP 8

implify the right side of the equation to get the final solution.
$x =19$ So, the solution to the proportion is $x =19$ .

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QuestionSolve the proportion using cross products: 34=9x−7\frac{3}{4}=\frac{9}{x-7}43​=x−79​. Find xxx.

Studdy Solution

STEP 1

Assumptions1. The given proportion is 34=9x−7\frac{3}{4}=\frac{9}{x-7}43​=x−79​. . We are asked to solve for xxx.3. The cross products of a proportion are equal.

STEP 2

We start by setting up the cross products of the proportion. The cross products of a proportion ab=cd\frac{a}{b}=\frac{c}{d}ba​=dc​ are a⋅da \cdot da⋅d and b⋅cb \cdot cb⋅c.⋅(x−7)=4⋅9 \cdot (x-7) =4 \cdot9⋅(x−7)=4⋅9

STEP 3

Now, simplify the right side of the equation.3⋅(x−7)=363 \cdot (x-7) =363⋅(x−7)=36

STEP 4

istribute the3 on the left side of the equation.3x−21=363x -21 =363x−21=36

STEP 5

Add21 to both sides of the equation to isolate the term with xxx on one side.3x=36+213x =36 +213x=36+21

STEP 6

implify the right side of the equation.3x=573x =573x=57

STEP 7

Finally, divide both sides of the equation by3 to solve for xxx.x=573x = \frac{57}{3}x=357​

STEP 8

implify the right side of the equation to get the final solution.x=19x =19x=19So, the solution to the proportion is x=19x =19x=19.

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QuestionSolve the proportion using cross products: $\frac{3}{4}=\frac{9}{x-7}$ . Find $x$ .

Assumptions1. The given proportion is $\frac{3}{4}=\frac{9}{x-7}$ . . We are asked to solve for $x$ .
3. The cross products of a proportion are equal.

We start by setting up the cross products of the proportion. The cross products of a proportion $\frac{a}{b}=\frac{c}{d}$ are $a \cdot d$ and $b \cdot c$ .
$\cdot (x-7) =4 \cdot9$

Now, simplify the right side of the equation.
$3 \cdot (x-7) =36$

istribute the3 on the left side of the equation.
$3x -21 =36$

Add21 to both sides of the equation to isolate the term with $x$ on one side.
$3x =36 +21$

implify the right side of the equation.
$3x =57$

Finally, divide both sides of the equation by3 to solve for $x$ .
$x = \frac{57}{3}$

implify the right side of the equation to get the final solution.
$x =19$ So, the solution to the proportion is $x =19$ .