Solve 6/x-3=1/1.25

$$\frac { 6 } { x - 3 } = \frac { 1 } { 1.25 }$$

Solve for x

$$x=10.5$$

Steps for Solving Linear Equation

Variable x cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by x-3.

$$6=\left(x-3\right)\times \frac{1}{1.25}$$

Expand \frac{1}{1.25} by multiplying both numerator and the denominator by 100.

$$6=\left(x-3\right)\times \frac{100}{125}$$

Reduce the fraction \frac{100}{125} to lowest terms by extracting and canceling out 25.

$$6=\left(x-3\right)\times \frac{4}{5}$$

Use the distributive property to multiply x-3 by \frac{4}{5}.

$$6=\frac{4}{5}x-\frac{12}{5}$$

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

$$\frac{4}{5}x-\frac{12}{5}=6$$

Add \frac{12}{5} to both sides.

$$\frac{4}{5}x=6+\frac{12}{5}$$

Add 6 and \frac{12}{5} to get \frac{42}{5}.

$$\frac{4}{5}x=\frac{42}{5}$$

Multiply both sides by \frac{5}{4}, the reciprocal of \frac{4}{5}.

$$x=\frac{42}{5}\times \frac{5}{4}$$

Multiply \frac{42}{5} and \frac{5}{4} to get \frac{21}{2}.

$$x=\frac{21}{2}$$