Solve 1/3(x+4)-2/5(x+1)=2

$$\frac{ 1 }{ 3 } (x+4)- \frac{ 2 }{ 5 } (x+1)=2$$

Solve for x

$$x=-16$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{3} by x+4.

$$\frac{1}{3}x+\frac{1}{3}\times 4-\frac{2}{5}\left(x+1\right)=2$$

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

$$\frac{1}{3}x+\frac{4}{3}-\frac{2}{5}\left(x+1\right)=2$$

Use the distributive property to multiply -\frac{2}{5} by x+1.

$$\frac{1}{3}x+\frac{4}{3}-\frac{2}{5}x-\frac{2}{5}=2$$

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

$$-\frac{1}{15}x+\frac{4}{3}-\frac{2}{5}=2$$

Least common multiple of 3 and 5 is 15. Convert \frac{4}{3} and \frac{2}{5} to fractions with denominator 15.

$$-\frac{1}{15}x+\frac{20}{15}-\frac{6}{15}=2$$

Since \frac{20}{15} and \frac{6}{15} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{15}x+\frac{20-6}{15}=2$$

Subtract 6 from 20 to get 14.

$$-\frac{1}{15}x+\frac{14}{15}=2$$

Subtract \frac{14}{15} from both sides.

$$-\frac{1}{15}x=2-\frac{14}{15}$$

Convert 2 to fraction \frac{30}{15}.

$$-\frac{1}{15}x=\frac{30}{15}-\frac{14}{15}$$

Since \frac{30}{15} and \frac{14}{15} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{15}x=\frac{30-14}{15}$$

Subtract 14 from 30 to get 16.

$$-\frac{1}{15}x=\frac{16}{15}$$

Multiply both sides by -15, the reciprocal of -\frac{1}{15}.

$$x=\frac{16}{15}\left(-15\right)$$

Express \frac{16}{15}\left(-15\right) as a single fraction.

$$x=\frac{16\left(-15\right)}{15}$$

Multiply 16 and -15 to get -240.

$$x=\frac{-240}{15}$$

Divide -240 by 15 to get -16.

$$x=-16$$