Solve 17(2-x)-5(x+12)/11-7x=8

$$\frac { 17 ( 2 - x ) - 5 ( x + 12 ) } { 11 - 7 x } = 8$$

Solve for x

$$x = \frac{57}{17} = 3\frac{6}{17} \approx 3.352941176$$

Steps for Solving Linear Equation

Variable x cannot be equal to \frac{11}{7} since division by zero is not defined. Multiply both sides of the equation by -7x+11.

$$17\left(2-x\right)-5\left(x+12\right)=8\left(-7x+11\right)$$

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

$$34-17x-5\left(x+12\right)=8\left(-7x+11\right)$$

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

$$34-17x-5x-60=8\left(-7x+11\right)$$

Combine -17x and -5x to get -22x.

$$34-22x-60=8\left(-7x+11\right)$$

Subtract 60 from 34 to get -26.

$$-26-22x=8\left(-7x+11\right)$$

Use the distributive property to multiply 8 by -7x+11.

$$-26-22x=-56x+88$$

Add 56x to both sides.

$$-26-22x+56x=88$$

Combine -22x and 56x to get 34x.

$$-26+34x=88$$

Add 26 to both sides.

$$34x=88+26$$

Add 88 and 26 to get 114.

$$34x=114$$

Divide both sides by 34.

$$x=\frac{114}{34}$$

Reduce the fraction \frac{114}{34} to lowest terms by extracting and canceling out 2.

$$x=\frac{57}{17}$$