Solve y = (2x + 5)/(3x - 7) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$y=\frac{2x+5}{3x-7}$$

Solve for x

$x=\frac{7y+5}{3y-2}$
$y\neq \frac{2}{3}$

Steps for Solving Linear Equation

Variable $x$ cannot be equal to $\frac{7}{3}$ since division by zero is not defined. Multiply both sides of the equation by $3x-7$.

$$y\left(3x-7\right)=2x+5$$

Use the distributive property to multiply $y$ by $3x-7$.

$$3yx-7y=2x+5$$

Subtract $2x$ from both sides.

$$3yx-7y-2x=5$$

Add $7y$ to both sides.

$$3yx-2x=5+7y$$

Combine all terms containing $x$.

$$\left(3y-2\right)x=5+7y$$

The equation is in standard form.

$$\left(3y-2\right)x=7y+5$$

Divide both sides by $3y-2$.

$$\frac{\left(3y-2\right)x}{3y-2}=\frac{7y+5}{3y-2}$$

Dividing by $3y-2$ undoes the multiplication by $3y-2$.

$$x=\frac{7y+5}{3y-2}$$

Variable $x$ cannot be equal to $\frac{7}{3}$.

$$x=\frac{7y+5}{3y-2}\text{, }x\neq \frac{7}{3}$$

Solve for y

$y=\frac{2x+5}{3x-7}$
$x\neq \frac{7}{3}$