Solve 1/3(x+2)=1/15x+4/3

$$\frac { 1 } { 3 } ( x + 2 ) = \frac { 1 } { 15 } x + \frac { 4 } { 3 }$$

Solve for x

$$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

Steps for Solving Linear Equation

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

$$\frac{1}{3}x+\frac{1}{3}\times 2=\frac{1}{15}x+\frac{4}{3}$$

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

$$\frac{1}{3}x+\frac{2}{3}=\frac{1}{15}x+\frac{4}{3}$$

Subtract \frac{1}{15}x from both sides.

$$\frac{1}{3}x+\frac{2}{3}-\frac{1}{15}x=\frac{4}{3}$$

Combine \frac{1}{3}x and -\frac{1}{15}x to get \frac{4}{15}x.

$$\frac{4}{15}x+\frac{2}{3}=\frac{4}{3}$$

Subtract \frac{2}{3} from both sides.

$$\frac{4}{15}x=\frac{4}{3}-\frac{2}{3}$$

Since \frac{4}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4}{15}x=\frac{4-2}{3}$$

Subtract 2 from 4 to get 2.

$$\frac{4}{15}x=\frac{2}{3}$$

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

$$x=\frac{2}{3}\times \frac{15}{4}$$

Multiply \frac{2}{3} times \frac{15}{4} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{2\times 15}{3\times 4}$$

Do the multiplications in the fraction \frac{2\times 15}{3\times 4}.

$$x=\frac{30}{12}$$

Reduce the fraction \frac{30}{12} to lowest terms by extracting and canceling out 6.

$$x=\frac{5}{2}$$