QuestionSolve for $x$ in the equation $\frac{x}{x+3}=\frac{5}{4}$ .

Studdy Solution

STEP 1

Assumptions1. The equation is $\frac{x}{x+3}=\frac{5}{4}$

STEP 2

To solve the equation, we need to get rid of the fractions. We can do this by cross-multiplying.
$x \times4 =5 \times (x +)$

STEP 3

Expand the right side of the equation.
$x =5x +15$

STEP 4

Rearrange the equation to isolate $x$ on one side. We can do this by subtracting $x$ from both sides of the equation.
$4x -x =15$

STEP 5

implify the left side of the equation.
$-x =15$

STEP 6

To solve for $x$ , we need to get rid of the negative sign. We can do this by multiplying both sides of the equation by $-1$ .
$x = -15$ So, the solution to the equation $\frac{x}{x+3}=\frac{5}{4}$ is $x = -15$ .

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QuestionSolve for $x$ in the equation $\frac{x}{x+3}=\frac{5}{4}$ .

Studdy Solution

STEP 1

Assumptions1. The equation is $\frac{x}{x+3}=\frac{5}{4}$

STEP 2

To solve the equation, we need to get rid of the fractions. We can do this by cross-multiplying.
$x \times4 =5 \times (x +)$

STEP 3

Expand the right side of the equation.
$x =5x +15$

STEP 4

Rearrange the equation to isolate $x$ on one side. We can do this by subtracting $x$ from both sides of the equation.
$4x -x =15$

STEP 5

implify the left side of the equation.
$-x =15$

STEP 6

To solve for $x$ , we need to get rid of the negative sign. We can do this by multiplying both sides of the equation by $-1$ .
$x = -15$ So, the solution to the equation $\frac{x}{x+3}=\frac{5}{4}$ is $x = -15$ .

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QuestionSolve for xxx in the equation xx+3=54\frac{x}{x+3}=\frac{5}{4}x+3x​=45​.

Studdy Solution

STEP 1

Assumptions1. The equation is xx+3=54\frac{x}{x+3}=\frac{5}{4}x+3x​=45​

STEP 2

To solve the equation, we need to get rid of the fractions. We can do this by cross-multiplying.x×4=5×(x+)x \times4 =5 \times (x +)x×4=5×(x+)

STEP 3

Expand the right side of the equation.x=5x+15x =5x +15x=5x+15

STEP 4

Rearrange the equation to isolate xxx on one side. We can do this by subtracting xxx from both sides of the equation.4x−x=154x -x =154x−x=15

STEP 5

implify the left side of the equation.−x=15-x =15−x=15

STEP 6

To solve for xxx, we need to get rid of the negative sign. We can do this by multiplying both sides of the equation by −1-1−1.x=−15x = -15x=−15So, the solution to the equation xx+3=54\frac{x}{x+3}=\frac{5}{4}x+3x​=45​ is x=−15x = -15x=−15.

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QuestionSolve for $x$ in the equation $\frac{x}{x+3}=\frac{5}{4}$ .

Assumptions1. The equation is $\frac{x}{x+3}=\frac{5}{4}$

To solve the equation, we need to get rid of the fractions. We can do this by cross-multiplying.
$x \times4 =5 \times (x +)$

Expand the right side of the equation.
$x =5x +15$

Rearrange the equation to isolate $x$ on one side. We can do this by subtracting $x$ from both sides of the equation.
$4x -x =15$

implify the left side of the equation.
$-x =15$

To solve for $x$ , we need to get rid of the negative sign. We can do this by multiplying both sides of the equation by $-1$ .
$x = -15$ So, the solution to the equation $\frac{x}{x+3}=\frac{5}{4}$ is $x = -15$ .