Solve 153/8div(23/4x+55/6)-11/2=frac{3}{4}

$$15 \frac { 3 } { 8 } \div ( 2 \frac { 3 } { 4 } x+ 5 \frac { 5 } { 6 } )- 1 \frac { 1 } { 2 } = \frac{ 3 }{ 4 }$$

Solve for x

$$x=\frac{4}{11}\approx 0.363636364$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4, the least common multiple of 2,4.

$$48\left(33x+70\right)^{-1}\times \frac{15\times 8+3}{8}-2\left(2+1\right)=3$$

Multiply 15 and 8 to get 120.

$$48\left(33x+70\right)^{-1}\times \frac{120+3}{8}-2\left(2+1\right)=3$$

Add 120 and 3 to get 123.

$$48\left(33x+70\right)^{-1}\times \frac{123}{8}-2\left(2+1\right)=3$$

Multiply 48 and \frac{123}{8} to get 738.

$$738\left(33x+70\right)^{-1}-2\left(2+1\right)=3$$

Add 2 and 1 to get 3.

$$738\left(33x+70\right)^{-1}-2\times 3=3$$

Multiply -2 and 3 to get -6.

$$738\left(33x+70\right)^{-1}-6=3$$

Add 6 to both sides.

$$738\left(33x+70\right)^{-1}=3+6$$

Add 3 and 6 to get 9.

$$738\left(33x+70\right)^{-1}=9$$

Divide both sides by 738.

$$\left(33x+70\right)^{-1}=\frac{9}{738}$$

Reduce the fraction \frac{9}{738} to lowest terms by extracting and canceling out 9.

$$\left(33x+70\right)^{-1}=\frac{1}{82}$$

Reorder the terms.

$$\frac{1}{33x+70}=\frac{1}{82}$$

Variable x cannot be equal to -\frac{70}{33} since division by zero is not defined. Multiply both sides of the equation by 82\left(33x+70\right), the least common multiple of 33x+70,82.

$$82=33x+70$$

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

$$33x+70=82$$

Subtract 70 from both sides.

$$33x=82-70$$

Subtract 70 from 82 to get 12.

$$33x=12$$

Divide both sides by 33.

$$x=\frac{12}{33}$$

Reduce the fraction \frac{12}{33} to lowest terms by extracting and canceling out 3.

$$x=\frac{4}{11}$$