Solve 3/4=39t+2/5x-1

$$\frac { 3 } { 4 } = \frac { 39 t + 2 } { 5 x - 1 }$$

Solve for t

$$t=\frac{5x}{52}-\frac{11}{156}$$

$$x\neq \frac{1}{5}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4\left(5x-1\right), the least common multiple of 4,5x-1.

$$3\left(5x-1\right)=4\left(39t+2\right)$$

Use the distributive property to multiply 3 by 5x-1.

$$15x-3=4\left(39t+2\right)$$

Use the distributive property to multiply 4 by 39t+2.

$$15x-3=156t+8$$

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

$$156t+8=15x-3$$

Subtract 8 from both sides.

$$156t=15x-3-8$$

Subtract 8 from -3 to get -11.

$$156t=15x-11$$

Divide both sides by 156.

$$\frac{156t}{156}=\frac{15x-11}{156}$$

Dividing by 156 undoes the multiplication by 156.

$$t=\frac{15x-11}{156}$$

Divide 15x-11 by 156.

$$t=\frac{5x}{52}-\frac{11}{156}$$

Solve for x

$$x=\frac{52t}{5}+\frac{11}{15}$$

$$t\neq -\frac{2}{39}$$

Steps for Solving Linear Equation

Variable x cannot be equal to \frac{1}{5} since division by zero is not defined. Multiply both sides of the equation by 4\left(5x-1\right), the least common multiple of 4,5x-1.

$$3\left(5x-1\right)=4\left(39t+2\right)$$

Use the distributive property to multiply 3 by 5x-1.

$$15x-3=4\left(39t+2\right)$$

Use the distributive property to multiply 4 by 39t+2.

$$15x-3=156t+8$$

Add 3 to both sides.

$$15x=156t+8+3$$

Add 8 and 3 to get 11.

$$15x=156t+11$$

Divide both sides by 15.

$$\frac{15x}{15}=\frac{156t+11}{15}$$

Dividing by 15 undoes the multiplication by 15.

$$x=\frac{156t+11}{15}$$

Divide 156t+11 by 15.

$$x=\frac{52t}{5}+\frac{11}{15}$$

Variable x cannot be equal to \frac{1}{5}.

$$x=\frac{52t}{5}+\frac{11}{15}\text{, }x\neq \frac{1}{5}$$