Solve (5-1/9):(1+2/9)=(7+3/4):x

$$( 5 - \frac { 1 } { 9 } ) : ( 1 + \frac { 2 } { 9 } ) = ( 7 + \frac { 3 } { 4 } ) : x$$

Solve for x

$$x = \frac{31}{16} = 1\frac{15}{16} = 1.9375$$

Steps for Solving Linear Equation

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

$$\frac{9}{11}x\left(5-\frac{1}{9}\right)=7+\frac{3}{4}$$

Convert 5 to fraction \frac{45}{9}.

$$\frac{9}{11}x\left(\frac{45}{9}-\frac{1}{9}\right)=7+\frac{3}{4}$$

Since \frac{45}{9} and \frac{1}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9}{11}x\times \frac{45-1}{9}=7+\frac{3}{4}$$

Subtract 1 from 45 to get 44.

$$\frac{9}{11}x\times \frac{44}{9}=7+\frac{3}{4}$$

Multiply \frac{9}{11} times \frac{44}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 44}{11\times 9}x=7+\frac{3}{4}$$

Cancel out 9 in both numerator and denominator.

$$\frac{44}{11}x=7+\frac{3}{4}$$

Divide 44 by 11 to get 4.

$$4x=7+\frac{3}{4}$$

Convert 7 to fraction \frac{28}{4}.

$$4x=\frac{28}{4}+\frac{3}{4}$$

Since \frac{28}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$4x=\frac{28+3}{4}$$

Add 28 and 3 to get 31.

$$4x=\frac{31}{4}$$

Divide both sides by 4.

$$x=\frac{\frac{31}{4}}{4}$$

Express \frac{\frac{31}{4}}{4} as a single fraction.

$$x=\frac{31}{4\times 4}$$

Multiply 4 and 4 to get 16.

$$x=\frac{31}{16}$$