Solve 3/(2b)-5=4-6a

$$3 / ( 2 b ) - 5 = 4 - 6 a$$

Solve for a

$$a=\frac{3}{2}-\frac{1}{4b}$$

$$b\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2b.

$$3+2b\left(-5\right)=2b\times 4-6a\times 2b$$

Multiply 2 and -5 to get -10.

$$3-10b=2b\times 4-6a\times 2b$$

Multiply 2 and 4 to get 8.

$$3-10b=8b-6a\times 2b$$

Multiply -6 and 2 to get -12.

$$3-10b=8b-12ab$$

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

$$8b-12ab=3-10b$$

Subtract 8b from both sides.

$$-12ab=3-10b-8b$$

Combine -10b and -8b to get -18b.

$$-12ab=3-18b$$

The equation is in standard form.

$$\left(-12b\right)a=3-18b$$

Divide both sides by -12b.

$$\frac{\left(-12b\right)a}{-12b}=\frac{3-18b}{-12b}$$

Dividing by -12b undoes the multiplication by -12b.

$$a=\frac{3-18b}{-12b}$$

Divide 3-18b by -12b.

$$a=\frac{3}{2}-\frac{1}{4b}$$

Solve for b

$$b=-\frac{1}{2\left(2a-3\right)}$$

$$a\neq \frac{3}{2}$$

Steps for Solving Linear Equation

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2b.

$$3+2b\left(-5\right)=2b\times 4-6a\times 2b$$

Multiply 2 and -5 to get -10.

$$3-10b=2b\times 4-6a\times 2b$$

Multiply 2 and 4 to get 8.

$$3-10b=8b-6a\times 2b$$

Multiply -6 and 2 to get -12.

$$3-10b=8b-12ab$$

Subtract 8b from both sides.

$$3-10b-8b=-12ab$$

Combine -10b and -8b to get -18b.

$$3-18b=-12ab$$

Add 12ab to both sides.

$$3-18b+12ab=0$$

Subtract 3 from both sides. Anything subtracted from zero gives its negation.

$$-18b+12ab=-3$$

Combine all terms containing b.

$$\left(-18+12a\right)b=-3$$

The equation is in standard form.

$$\left(12a-18\right)b=-3$$

Divide both sides by -18+12a.

$$\frac{\left(12a-18\right)b}{12a-18}=-\frac{3}{12a-18}$$

Dividing by -18+12a undoes the multiplication by -18+12a.

$$b=-\frac{3}{12a-18}$$

Divide -3 by -18+12a.

$$b=-\frac{1}{2\left(2a-3\right)}$$

Variable b cannot be equal to 0.

$$b=-\frac{1}{2\left(2a-3\right)}\text{, }b\neq 0$$