Solve 15/28:(8-31/2x)=42/7

$$\frac { 15 } { 28 } : ( 8 - 3 \frac { 1 } { 2 } x ) = 4 \frac { 2 } { 7 }$$

Solve for x

$$x = \frac{9}{4} = 2\frac{1}{4} = 2.25$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 7.

$$14\left(16-7x\right)^{-1}\times \frac{15}{28}=4\times 7+2$$

Multiply 14 and \frac{15}{28} to get \frac{15}{2}.

$$\frac{15}{2}\left(16-7x\right)^{-1}=4\times 7+2$$

Multiply 4 and 7 to get 28.

$$\frac{15}{2}\left(16-7x\right)^{-1}=28+2$$

Add 28 and 2 to get 30.

$$\frac{15}{2}\left(16-7x\right)^{-1}=30$$

Multiply both sides by \frac{2}{15}, the reciprocal of \frac{15}{2}.

$$\left(16-7x\right)^{-1}=30\times \frac{2}{15}$$

Multiply 30 and \frac{2}{15} to get 4.

$$\left(16-7x\right)^{-1}=4$$

Reorder the terms.

$$\frac{1}{-7x+16}=4$$

Variable x cannot be equal to \frac{16}{7} since division by zero is not defined. Multiply both sides of the equation by -7x+16.

$$1=4\left(-7x+16\right)$$

Use the distributive property to multiply 4 by -7x+16.

$$1=-28x+64$$

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

$$-28x+64=1$$

Subtract 64 from both sides.

$$-28x=1-64$$

Subtract 64 from 1 to get -63.

$$-28x=-63$$

Divide both sides by -28.

$$x=\frac{-63}{-28}$$

Reduce the fraction \frac{-63}{-28} to lowest terms by extracting and canceling out -7.

$$x=\frac{9}{4}$$