Solve 9*2y-3/14-3y-5/2=x+3/4

$$9 \cdot \frac { 2 y - 3 } { 14 } - \frac { 3 y - 5 } { 2 } = x + \frac { 3 } { 4 }$$

Solve for x

$$x=-\frac{3y}{14}-\frac{5}{28}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 28, the least common multiple of 14,2,4.

$$18\left(2y-3\right)-14\left(3y-5\right)=28x+21$$

Use the distributive property to multiply 18 by 2y-3.

$$36y-54-14\left(3y-5\right)=28x+21$$

Use the distributive property to multiply -14 by 3y-5.

$$36y-54-42y+70=28x+21$$

Combine 36y and -42y to get -6y.

$$-6y-54+70=28x+21$$

Add -54 and 70 to get 16.

$$-6y+16=28x+21$$

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

$$28x+21=-6y+16$$

Subtract 21 from both sides.

$$28x=-6y+16-21$$

Subtract 21 from 16 to get -5.

$$28x=-6y-5$$

Divide both sides by 28.

$$\frac{28x}{28}=\frac{-6y-5}{28}$$

Dividing by 28 undoes the multiplication by 28.

$$x=\frac{-6y-5}{28}$$

Divide -6y-5 by 28.

$$x=-\frac{3y}{14}-\frac{5}{28}$$

Solve for y

$$y=-\frac{14x}{3}-\frac{5}{6}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 28, the least common multiple of 14,2,4.

$$18\left(2y-3\right)-14\left(3y-5\right)=28x+21$$

Use the distributive property to multiply 18 by 2y-3.

$$36y-54-14\left(3y-5\right)=28x+21$$

Use the distributive property to multiply -14 by 3y-5.

$$36y-54-42y+70=28x+21$$

Combine 36y and -42y to get -6y.

$$-6y-54+70=28x+21$$

Add -54 and 70 to get 16.

$$-6y+16=28x+21$$

Subtract 16 from both sides.

$$-6y=28x+21-16$$

Subtract 16 from 21 to get 5.

$$-6y=28x+5$$

Divide both sides by -6.

$$\frac{-6y}{-6}=\frac{28x+5}{-6}$$

Dividing by -6 undoes the multiplication by -6.

$$y=\frac{28x+5}{-6}$$

Divide 28x+5 by -6.

$$y=-\frac{14x}{3}-\frac{5}{6}$$