Solve y-11=5/2(x-7)

$$y - 11 = \frac { 5 } { 2 } ( x - 7 )$$

Solve for x

$$x=\frac{2y+13}{5}$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{5}{2} by x-7.

$$y-11=\frac{5}{2}x-\frac{35}{2}$$

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

$$\frac{5}{2}x-\frac{35}{2}=y-11$$

Add \frac{35}{2} to both sides.

$$\frac{5}{2}x=y-11+\frac{35}{2}$$

Add -11 and \frac{35}{2} to get \frac{13}{2}.

$$\frac{5}{2}x=y+\frac{13}{2}$$

Divide both sides of the equation by \frac{5}{2}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{5}{2}x}{\frac{5}{2}}=\frac{y+\frac{13}{2}}{\frac{5}{2}}$$

Dividing by \frac{5}{2} undoes the multiplication by \frac{5}{2}.

$$x=\frac{y+\frac{13}{2}}{\frac{5}{2}}$$

Divide y+\frac{13}{2} by \frac{5}{2} by multiplying y+\frac{13}{2} by the reciprocal of \frac{5}{2}.

$$x=\frac{2y+13}{5}$$

Solve for y

$$y=\frac{5x-13}{2}$$

Solution Steps

Use the distributive property to multiply \frac{5}{2} by x-7.

$$y-11=\frac{5}{2}x-\frac{35}{2}$$

Add 11 to both sides.

$$y=\frac{5}{2}x-\frac{35}{2}+11$$

Add -\frac{35}{2} and 11 to get -\frac{13}{2}.

$$y=\frac{5}{2}x-\frac{13}{2}$$