Solve 1/3(x+3)=1/5(x-3)

$$\frac { 1 } { 3 } ( x + 3 ) = \frac { 1 } { 5 } ( x - 3 )$$

Solve for x

$$x=-12$$

Steps for Solving Linear Equation

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

$$\frac{1}{3}x+\frac{1}{3}\times 3=\frac{1}{5}\left(x-3\right)$$

Cancel out 3 and 3.

$$\frac{1}{3}x+1=\frac{1}{5}\left(x-3\right)$$

Use the distributive property to multiply \frac{1}{5} by x-3.

$$\frac{1}{3}x+1=\frac{1}{5}x+\frac{1}{5}\left(-3\right)$$

Multiply \frac{1}{5} and -3 to get \frac{-3}{5}.

$$\frac{1}{3}x+1=\frac{1}{5}x+\frac{-3}{5}$$

Fraction \frac{-3}{5} can be rewritten as -\frac{3}{5} by extracting the negative sign.

$$\frac{1}{3}x+1=\frac{1}{5}x-\frac{3}{5}$$

Subtract \frac{1}{5}x from both sides.

$$\frac{1}{3}x+1-\frac{1}{5}x=-\frac{3}{5}$$

Combine \frac{1}{3}x and -\frac{1}{5}x to get \frac{2}{15}x.

$$\frac{2}{15}x+1=-\frac{3}{5}$$

Subtract 1 from both sides.

$$\frac{2}{15}x=-\frac{3}{5}-1$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{2}{15}x=-\frac{3}{5}-\frac{5}{5}$$

Since -\frac{3}{5} and \frac{5}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{15}x=\frac{-3-5}{5}$$

Subtract 5 from -3 to get -8.

$$\frac{2}{15}x=-\frac{8}{5}$$

Multiply both sides by \frac{15}{2}, the reciprocal of \frac{2}{15}.

$$x=-\frac{8}{5}\times \frac{15}{2}$$

Multiply -\frac{8}{5} times \frac{15}{2} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-8\times 15}{5\times 2}$$

Do the multiplications in the fraction \frac{-8\times 15}{5\times 2}.

$$x=\frac{-120}{10}$$

Divide -120 by 10 to get -12.

$$x=-12$$