Solve 9/2(8x+4)=14(10-x)

$$\frac { 9 } { 2 } ( 8 x + 4 ) = 14 ( 10 - x )$$

Solve for x

$$x = \frac{61}{25} = 2\frac{11}{25} = 2.44$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{9}{2} by 8x+4.

$$\frac{9}{2}\times 8x+\frac{9}{2}\times 4=14\left(10-x\right)$$

Express \frac{9}{2}\times 8 as a single fraction.

$$\frac{9\times 8}{2}x+\frac{9}{2}\times 4=14\left(10-x\right)$$

Multiply 9 and 8 to get 72.

$$\frac{72}{2}x+\frac{9}{2}\times 4=14\left(10-x\right)$$

Divide 72 by 2 to get 36.

$$36x+\frac{9}{2}\times 4=14\left(10-x\right)$$

Express \frac{9}{2}\times 4 as a single fraction.

$$36x+\frac{9\times 4}{2}=14\left(10-x\right)$$

Multiply 9 and 4 to get 36.

$$36x+\frac{36}{2}=14\left(10-x\right)$$

Divide 36 by 2 to get 18.

$$36x+18=14\left(10-x\right)$$

Use the distributive property to multiply 14 by 10-x.

$$36x+18=140-14x$$

Add 14x to both sides.

$$36x+18+14x=140$$

Combine 36x and 14x to get 50x.

$$50x+18=140$$

Subtract 18 from both sides.

$$50x=140-18$$

Subtract 18 from 140 to get 122.

$$50x=122$$

Divide both sides by 50.

$$x=\frac{122}{50}$$

Reduce the fraction \frac{122}{50} to lowest terms by extracting and canceling out 2.

$$x=\frac{61}{25}$$