Solve 5(3x-1)/6-x=-13/12Theta2x+7/4

$$\frac { 5 ( 3 x - 1 ) } { 6 } - x = - \frac { 13 } { 12 } \Theta \frac { 2 x + 7 } { 4 }$$

Solve for x

$$x=-\frac{91\Theta -40}{2\left(13\Theta +36\right)}$$

$$\Theta \neq -\frac{36}{13}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 6,12,4.

$$2\times 5\left(3x-1\right)-12x=-\frac{13}{4}\Theta \left(2x+7\right)$$

Multiply 2 and 5 to get 10.

$$10\left(3x-1\right)-12x=-\frac{13}{4}\Theta \left(2x+7\right)$$

Use the distributive property to multiply 10 by 3x-1.

$$30x-10-12x=-\frac{13}{4}\Theta \left(2x+7\right)$$

Combine 30x and -12x to get 18x.

$$18x-10=-\frac{13}{4}\Theta \left(2x+7\right)$$

Use the distributive property to multiply -\frac{13}{4}\Theta by 2x+7.

$$18x-10=-\frac{13}{2}\Theta x-\frac{91}{4}\Theta$$

Add \frac{13}{2}\Theta x to both sides.

$$18x-10+\frac{13}{2}\Theta x=-\frac{91}{4}\Theta$$

Add 10 to both sides.

$$18x+\frac{13}{2}\Theta x=-\frac{91}{4}\Theta +10$$

Combine all terms containing x.

$$\left(18+\frac{13}{2}\Theta \right)x=-\frac{91}{4}\Theta +10$$

The equation is in standard form.

$$\left(\frac{13\Theta }{2}+18\right)x=-\frac{91\Theta }{4}+10$$

Divide both sides by 18+\frac{13}{2}\Theta .

$$\frac{\left(\frac{13\Theta }{2}+18\right)x}{\frac{13\Theta }{2}+18}=\frac{-\frac{91\Theta }{4}+10}{\frac{13\Theta }{2}+18}$$

Dividing by 18+\frac{13}{2}\Theta undoes the multiplication by 18+\frac{13}{2}\Theta .

$$x=\frac{-\frac{91\Theta }{4}+10}{\frac{13\Theta }{2}+18}$$

Divide -\frac{91\Theta }{4}+10 by 18+\frac{13}{2}\Theta .

$$x=\frac{40-91\Theta }{2\left(13\Theta +36\right)}$$

Solve for Θ

$$\Theta =\frac{8\left(5-9x\right)}{13\left(2x+7\right)}$$

$$x\neq -\frac{7}{2}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 6,12,4.

$$2\times 5\left(3x-1\right)-12x=-\frac{13}{4}\Theta \left(2x+7\right)$$

Multiply 2 and 5 to get 10.

$$10\left(3x-1\right)-12x=-\frac{13}{4}\Theta \left(2x+7\right)$$

Use the distributive property to multiply 10 by 3x-1.

$$30x-10-12x=-\frac{13}{4}\Theta \left(2x+7\right)$$

Combine 30x and -12x to get 18x.

$$18x-10=-\frac{13}{4}\Theta \left(2x+7\right)$$

Use the distributive property to multiply -\frac{13}{4}\Theta by 2x+7.

$$18x-10=-\frac{13}{2}x\Theta -\frac{91}{4}\Theta$$

Swap sides so that all variable terms are on the left hand side.

$$-\frac{13}{2}x\Theta -\frac{91}{4}\Theta =18x-10$$

Combine all terms containing \Theta .

$$\left(-\frac{13}{2}x-\frac{91}{4}\right)\Theta =18x-10$$

The equation is in standard form.

$$\left(-\frac{13x}{2}-\frac{91}{4}\right)\Theta =18x-10$$

Divide both sides by -\frac{13}{2}x-\frac{91}{4}.

$$\frac{\left(-\frac{13x}{2}-\frac{91}{4}\right)\Theta }{-\frac{13x}{2}-\frac{91}{4}}=\frac{18x-10}{-\frac{13x}{2}-\frac{91}{4}}$$

Dividing by -\frac{13}{2}x-\frac{91}{4} undoes the multiplication by -\frac{13}{2}x-\frac{91}{4}.

$$\Theta =\frac{18x-10}{-\frac{13x}{2}-\frac{91}{4}}$$

Divide 18x-10 by -\frac{13}{2}x-\frac{91}{4}.

$$\Theta =-\frac{8\left(9x-5\right)}{13\left(2x+7\right)}$$