Solve 17(2-3x)-5(12-x)=8(1-7x)

$$17(2-3x)-5(12-x)=8(1-7x)$$

Solve for x

$$x = \frac{17}{5} = 3\frac{2}{5} = 3.4$$

Steps for Solving Linear Equation

Use the distributive property to multiply 17 by 2-3x.

$$34-51x-5\left(12-x\right)=8\left(1-7x\right)$$

Use the distributive property to multiply -5 by 12-x.

$$34-51x-60+5x=8\left(1-7x\right)$$

Subtract 60 from 34 to get -26.

$$-26-51x+5x=8\left(1-7x\right)$$

Combine -51x and 5x to get -46x.

$$-26-46x=8\left(1-7x\right)$$

Use the distributive property to multiply 8 by 1-7x.

$$-26-46x=8-56x$$

Add 56x to both sides.

$$-26-46x+56x=8$$

Combine -46x and 56x to get 10x.

$$-26+10x=8$$

Add 26 to both sides.

$$10x=8+26$$

Add 8 and 26 to get 34.

$$10x=34$$

Divide both sides by 10.

$$x=\frac{34}{10}$$

Reduce the fraction \frac{34}{10} to lowest terms by extracting and canceling out 2.

$$x=\frac{17}{5}$$