Solve 1/10(a+1)=1/6(2-a)

$$\frac { 1 } { 10 } ( a + 1 ) = \frac { 1 } { 6 } ( 2 - a )$$

Solve for a

$$a=\frac{7}{8}=0.875$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{10} by a+1.

$$\frac{1}{10}a+\frac{1}{10}=\frac{1}{6}\left(2-a\right)$$

Use the distributive property to multiply \frac{1}{6} by 2-a.

$$\frac{1}{10}a+\frac{1}{10}=\frac{1}{6}\times 2+\frac{1}{6}\left(-1\right)a$$

Multiply \frac{1}{6} and 2 to get \frac{2}{6}.

$$\frac{1}{10}a+\frac{1}{10}=\frac{2}{6}+\frac{1}{6}\left(-1\right)a$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$\frac{1}{10}a+\frac{1}{10}=\frac{1}{3}+\frac{1}{6}\left(-1\right)a$$

Multiply \frac{1}{6} and -1 to get -\frac{1}{6}.

$$\frac{1}{10}a+\frac{1}{10}=\frac{1}{3}-\frac{1}{6}a$$

Add \frac{1}{6}a to both sides.

$$\frac{1}{10}a+\frac{1}{10}+\frac{1}{6}a=\frac{1}{3}$$

Combine \frac{1}{10}a and \frac{1}{6}a to get \frac{4}{15}a.

$$\frac{4}{15}a+\frac{1}{10}=\frac{1}{3}$$

Subtract \frac{1}{10} from both sides.

$$\frac{4}{15}a=\frac{1}{3}-\frac{1}{10}$$

Least common multiple of 3 and 10 is 30. Convert \frac{1}{3} and \frac{1}{10} to fractions with denominator 30.

$$\frac{4}{15}a=\frac{10}{30}-\frac{3}{30}$$

Since \frac{10}{30} and \frac{3}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4}{15}a=\frac{10-3}{30}$$

Subtract 3 from 10 to get 7.

$$\frac{4}{15}a=\frac{7}{30}$$

Multiply both sides by \frac{15}{4}, the reciprocal of \frac{4}{15}.

$$a=\frac{7}{30}\times \frac{15}{4}$$

Multiply \frac{7}{30} times \frac{15}{4} by multiplying numerator times numerator and denominator times denominator.

$$a=\frac{7\times 15}{30\times 4}$$

Do the multiplications in the fraction \frac{7\times 15}{30\times 4}.

$$a=\frac{105}{120}$$

Reduce the fraction \frac{105}{120} to lowest terms by extracting and canceling out 15.

$$a=\frac{7}{8}$$