Solve 5/8(p+3)-2=1/4(2p-3)+11/16

$$\frac { 5 } { 8 } ( p + 3 ) - 2 = \frac { 1 } { 4 } ( 2 p - 3 ) + \frac { 11 } { 16 }$$

Solve for p

$$p=\frac{1}{2}=0.5$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{5}{8} by p+3.

$$\frac{5}{8}p+\frac{5}{8}\times 3-2=\frac{1}{4}\left(2p-3\right)+\frac{11}{16}$$

Express \frac{5}{8}\times 3 as a single fraction.

$$\frac{5}{8}p+\frac{5\times 3}{8}-2=\frac{1}{4}\left(2p-3\right)+\frac{11}{16}$$

Multiply 5 and 3 to get 15.

$$\frac{5}{8}p+\frac{15}{8}-2=\frac{1}{4}\left(2p-3\right)+\frac{11}{16}$$

Convert 2 to fraction \frac{16}{8}.

$$\frac{5}{8}p+\frac{15}{8}-\frac{16}{8}=\frac{1}{4}\left(2p-3\right)+\frac{11}{16}$$

Since \frac{15}{8} and \frac{16}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{8}p+\frac{15-16}{8}=\frac{1}{4}\left(2p-3\right)+\frac{11}{16}$$

Subtract 16 from 15 to get -1.

$$\frac{5}{8}p-\frac{1}{8}=\frac{1}{4}\left(2p-3\right)+\frac{11}{16}$$

Use the distributive property to multiply \frac{1}{4} by 2p-3.

$$\frac{5}{8}p-\frac{1}{8}=\frac{1}{4}\times 2p+\frac{1}{4}\left(-3\right)+\frac{11}{16}$$

Multiply \frac{1}{4} and 2 to get \frac{2}{4}.

$$\frac{5}{8}p-\frac{1}{8}=\frac{2}{4}p+\frac{1}{4}\left(-3\right)+\frac{11}{16}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{5}{8}p-\frac{1}{8}=\frac{1}{2}p+\frac{1}{4}\left(-3\right)+\frac{11}{16}$$

Multiply \frac{1}{4} and -3 to get \frac{-3}{4}.

$$\frac{5}{8}p-\frac{1}{8}=\frac{1}{2}p+\frac{-3}{4}+\frac{11}{16}$$

Fraction \frac{-3}{4} can be rewritten as -\frac{3}{4} by extracting the negative sign.

$$\frac{5}{8}p-\frac{1}{8}=\frac{1}{2}p-\frac{3}{4}+\frac{11}{16}$$

Least common multiple of 4 and 16 is 16. Convert -\frac{3}{4} and \frac{11}{16} to fractions with denominator 16.

$$\frac{5}{8}p-\frac{1}{8}=\frac{1}{2}p-\frac{12}{16}+\frac{11}{16}$$

Since -\frac{12}{16} and \frac{11}{16} have the same denominator, add them by adding their numerators.

$$\frac{5}{8}p-\frac{1}{8}=\frac{1}{2}p+\frac{-12+11}{16}$$

Add -12 and 11 to get -1.

$$\frac{5}{8}p-\frac{1}{8}=\frac{1}{2}p-\frac{1}{16}$$

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

$$\frac{5}{8}p-\frac{1}{8}-\frac{1}{2}p=-\frac{1}{16}$$

Combine \frac{5}{8}p and -\frac{1}{2}p to get \frac{1}{8}p.

$$\frac{1}{8}p-\frac{1}{8}=-\frac{1}{16}$$

Add \frac{1}{8} to both sides.

$$\frac{1}{8}p=-\frac{1}{16}+\frac{1}{8}$$

Least common multiple of 16 and 8 is 16. Convert -\frac{1}{16} and \frac{1}{8} to fractions with denominator 16.

$$\frac{1}{8}p=-\frac{1}{16}+\frac{2}{16}$$

Since -\frac{1}{16} and \frac{2}{16} have the same denominator, add them by adding their numerators.

$$\frac{1}{8}p=\frac{-1+2}{16}$$

Add -1 and 2 to get 1.

$$\frac{1}{8}p=\frac{1}{16}$$

Multiply both sides by 8, the reciprocal of \frac{1}{8}.

$$p=\frac{1}{16}\times 8$$

Multiply \frac{1}{16} and 8 to get \frac{8}{16}.

$$p=\frac{8}{16}$$

Reduce the fraction \frac{8}{16} to lowest terms by extracting and canceling out 8.

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