Solve y=7(a-4)-5/2-6(a-4)

$$y = \frac { 7 ( a - 4 ) - 5 } { 2 - 6 ( a - 4 ) }$$

Solve for a

$$a=\frac{26y+33}{6y+7}$$

$$y\neq -\frac{7}{6}$$

Steps for Solving Linear Equation

Variable a cannot be equal to \frac{13}{3} since division by zero is not defined. Multiply both sides of the equation by 2\left(-3a+13\right).

$$y\times 2\left(-3a+13\right)=7\left(a-4\right)-5$$

Use the distributive property to multiply y\times 2 by -3a+13.

$$-6ay+13y\times 2=7\left(a-4\right)-5$$

Multiply 13 and 2 to get 26.

$$-6ay+26y=7\left(a-4\right)-5$$

Use the distributive property to multiply 7 by a-4.

$$-6ay+26y=7a-28-5$$

Subtract 5 from -28 to get -33.

$$-6ay+26y=7a-33$$

Subtract 7a from both sides.

$$-6ay+26y-7a=-33$$

Subtract 26y from both sides.

$$-6ay-7a=-33-26y$$

Combine all terms containing a.

$$\left(-6y-7\right)a=-33-26y$$

The equation is in standard form.

$$\left(-6y-7\right)a=-26y-33$$

Divide both sides by -6y-7.

$$\frac{\left(-6y-7\right)a}{-6y-7}=\frac{-26y-33}{-6y-7}$$

Dividing by -6y-7 undoes the multiplication by -6y-7.

$$a=\frac{-26y-33}{-6y-7}$$

Divide -26y-33 by -6y-7.

$$a=\frac{26y+33}{6y+7}$$

Variable a cannot be equal to \frac{13}{3}.

$$a=\frac{26y+33}{6y+7}\text{, }a\neq \frac{13}{3}$$

Solve for y

$$y=-\frac{33-7a}{2\left(13-3a\right)}$$

$$a\neq \frac{13}{3}$$