Solve 2(3p-1)+3(p+1)=1/2(p+3)-1

$$2 ( 3 p - 1 ) + 3 ( p + 1 ) = \frac { 1 } { 2 } ( p + 3 ) - 1$$

Solve for p

$$p=-\frac{1}{17}\approx -0.058823529$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by 3p-1.

$$6p-2+3\left(p+1\right)=\frac{1}{2}\left(p+3\right)-1$$

Use the distributive property to multiply 3 by p+1.

$$6p-2+3p+3=\frac{1}{2}\left(p+3\right)-1$$

Combine 6p and 3p to get 9p.

$$9p-2+3=\frac{1}{2}\left(p+3\right)-1$$

Add -2 and 3 to get 1.

$$9p+1=\frac{1}{2}\left(p+3\right)-1$$

Use the distributive property to multiply \frac{1}{2} by p+3.

$$9p+1=\frac{1}{2}p+\frac{1}{2}\times 3-1$$

Multiply \frac{1}{2} and 3 to get \frac{3}{2}.

$$9p+1=\frac{1}{2}p+\frac{3}{2}-1$$

Convert 1 to fraction \frac{2}{2}.

$$9p+1=\frac{1}{2}p+\frac{3}{2}-\frac{2}{2}$$

Since \frac{3}{2} and \frac{2}{2} have the same denominator, subtract them by subtracting their numerators.

$$9p+1=\frac{1}{2}p+\frac{3-2}{2}$$

Subtract 2 from 3 to get 1.

$$9p+1=\frac{1}{2}p+\frac{1}{2}$$

Subtract \frac{1}{2}p from both sides.

$$9p+1-\frac{1}{2}p=\frac{1}{2}$$

Combine 9p and -\frac{1}{2}p to get \frac{17}{2}p.

$$\frac{17}{2}p+1=\frac{1}{2}$$

Subtract 1 from both sides.

$$\frac{17}{2}p=\frac{1}{2}-1$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{17}{2}p=\frac{1}{2}-\frac{2}{2}$$

Since \frac{1}{2} and \frac{2}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{17}{2}p=\frac{1-2}{2}$$

Subtract 2 from 1 to get -1.

$$\frac{17}{2}p=-\frac{1}{2}$$

Multiply both sides by \frac{2}{17}, the reciprocal of \frac{17}{2}.

$$p=-\frac{1}{2}\times \frac{2}{17}$$

Multiply -\frac{1}{2} times \frac{2}{17} by multiplying numerator times numerator and denominator times denominator.

$$p=\frac{-2}{2\times 17}$$

Cancel out 2 in both numerator and denominator.

$$p=\frac{-1}{17}$$

Fraction \frac{-1}{17} can be rewritten as -\frac{1}{17} by extracting the negative sign.

$$p=-\frac{1}{17}$$