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

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

Solve for x

$$x=3y-5$$

Steps for Solving Linear Equation

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

$$9\left(2y-3\right)-2\left(3y-5\right)=4x+3$$

Use the distributive property to multiply 9 by 2y-3.

$$18y-27-2\left(3y-5\right)=4x+3$$

Use the distributive property to multiply -2 by 3y-5.

$$18y-27-6y+10=4x+3$$

Combine 18y and -6y to get 12y.

$$12y-27+10=4x+3$$

Add -27 and 10 to get -17.

$$12y-17=4x+3$$

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

$$4x+3=12y-17$$

Subtract 3 from both sides.

$$4x=12y-17-3$$

Subtract 3 from -17 to get -20.

$$4x=12y-20$$

Divide both sides by 4.

$$\frac{4x}{4}=\frac{12y-20}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x=\frac{12y-20}{4}$$

Divide 12y-20 by 4.

$$x=3y-5$$

Solve for y

$$y=\frac{x+5}{3}$$

Steps for Solving Linear Equation

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

$$9\left(2y-3\right)-2\left(3y-5\right)=4x+3$$

Use the distributive property to multiply 9 by 2y-3.

$$18y-27-2\left(3y-5\right)=4x+3$$

Use the distributive property to multiply -2 by 3y-5.

$$18y-27-6y+10=4x+3$$

Combine 18y and -6y to get 12y.

$$12y-27+10=4x+3$$

Add -27 and 10 to get -17.

$$12y-17=4x+3$$

Add 17 to both sides.

$$12y=4x+3+17$$

Add 3 and 17 to get 20.

$$12y=4x+20$$

Divide both sides by 12.

$$\frac{12y}{12}=\frac{4x+20}{12}$$

Dividing by 12 undoes the multiplication by 12.

$$y=\frac{4x+20}{12}$$

Divide 20+4x by 12.

$$y=\frac{x+5}{3}$$