Solve y-5=5/4[x-(-2)]

$$y - 5 = \frac { 5 } { 4 } [ x - ( - 2 ) ]$$

Solve for x

$$x=\frac{4y}{5}-6$$

Steps for Solving Linear Equation

The opposite of -2 is 2.

$$y-5=\frac{5}{4}\left(x+2\right)$$

Use the distributive property to multiply \frac{5}{4} by x+2.

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

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

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

Subtract \frac{5}{2} from both sides.

$$\frac{5}{4}x=y-5-\frac{5}{2}$$

Subtract \frac{5}{2} from -5 to get -\frac{15}{2}.

$$\frac{5}{4}x=y-\frac{15}{2}$$

Divide both sides of the equation by \frac{5}{4}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{5}{4}x}{\frac{5}{4}}=\frac{y-\frac{15}{2}}{\frac{5}{4}}$$

Dividing by \frac{5}{4} undoes the multiplication by \frac{5}{4}.

$$x=\frac{y-\frac{15}{2}}{\frac{5}{4}}$$

Divide y-\frac{15}{2} by \frac{5}{4} by multiplying y-\frac{15}{2} by the reciprocal of \frac{5}{4}.

$$x=\frac{4y}{5}-6$$

Solve for y

$$y=\frac{5\left(x+6\right)}{4}$$

Solution Steps

The opposite of -2 is 2.

$$y-5=\frac{5}{4}\left(x+2\right)$$

Use the distributive property to multiply \frac{5}{4} by x+2.

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

Add 5 to both sides.

$$y=\frac{5}{4}x+\frac{5}{2}+5$$

Add \frac{5}{2} and 5 to get \frac{15}{2}.

$$y=\frac{5}{4}x+\frac{15}{2}$$