Solve 15.38=678+14x/43+x

$$15.38 = \frac{ 678+14x }{ 43+x }$$

Solve for x

$$x = \frac{833}{69} = 12\frac{5}{69} \approx 12.072463768$$

Steps for Solving Linear Equation

Variable x cannot be equal to -43 since division by zero is not defined. Multiply both sides of the equation by x+43.

$$15.38\left(x+43\right)=678+14x$$

Use the distributive property to multiply 15.38 by x+43.

$$15.38x+661.34=678+14x$$

Subtract 14x from both sides.

$$15.38x+661.34-14x=678$$

Combine 15.38x and -14x to get 1.38x.

$$1.38x+661.34=678$$

Subtract 661.34 from both sides.

$$1.38x=678-661.34$$

Subtract 661.34 from 678 to get 16.66.

$$1.38x=16.66$$

Divide both sides by 1.38.

$$x=\frac{16.66}{1.38}$$

Expand \frac{16.66}{1.38} by multiplying both numerator and the denominator by 100.

$$x=\frac{1666}{138}$$

Reduce the fraction \frac{1666}{138} to lowest terms by extracting and canceling out 2.

$$x=\frac{833}{69}$$