Solve 1/14(5p+4p-7/2)-8p=3(1-8p/4+p)

$$\frac { 1 } { 14 } ( 5 p + \frac { 4 p - 7 } { 2 } ) - 8 p = 3 ( \frac { 1 - 8 p } { 4 } + p )$$

Solve for p

$$p=-\frac{2}{9}\approx -0.222222222$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 28, the least common multiple of 14,2,4.

$$2\left(5p+\frac{4p-7}{2}\right)-224p=84\left(\frac{1-8p}{4}+p\right)$$

Use the distributive property to multiply 2 by 5p+\frac{4p-7}{2}.

$$10p+2\times \frac{4p-7}{2}-224p=84\left(\frac{1-8p}{4}+p\right)$$

Express 2\times \frac{4p-7}{2} as a single fraction.

$$10p+\frac{2\left(4p-7\right)}{2}-224p=84\left(\frac{1-8p}{4}+p\right)$$

Cancel out 2 and 2.

$$10p+4p-7-224p=84\left(\frac{1-8p}{4}+p\right)$$

Combine 10p and 4p to get 14p.

$$14p-7-224p=84\left(\frac{1-8p}{4}+p\right)$$

Combine 14p and -224p to get -210p.

$$-210p-7=84\left(\frac{1-8p}{4}+p\right)$$

Use the distributive property to multiply 84 by \frac{1-8p}{4}+p.

$$-210p-7=84\times \frac{1-8p}{4}+84p$$

Cancel out 4, the greatest common factor in 84 and 4.

$$-210p-7=21\left(1-8p\right)+84p$$

Use the distributive property to multiply 21 by 1-8p.

$$-210p-7=21-168p+84p$$

Combine -168p and 84p to get -84p.

$$-210p-7=21-84p$$

Add 84p to both sides.

$$-210p-7+84p=21$$

Combine -210p and 84p to get -126p.

$$-126p-7=21$$

Add 7 to both sides.

$$-126p=21+7$$

Add 21 and 7 to get 28.

$$-126p=28$$

Divide both sides by -126.

$$p=\frac{28}{-126}$$

Reduce the fraction \frac{28}{-126} to lowest terms by extracting and canceling out 14.

$$p=-\frac{2}{9}$$