Solve 1/5(x+5)<1/6(3x+4)

$$\frac { 1 } { 5 } ( x + 5 ) < \frac { 1 } { 6 } ( 3 x + 4 )$$

Solve for x

$$x>\frac{10}{9}$$

Solution Steps

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

$$\frac{1}{5}x+\frac{1}{5}\times 5<\frac{1}{6}\left(3x+4\right)$$

Cancel out 5 and 5.

$$\frac{1}{5}x+1<\frac{1}{6}\left(3x+4\right)$$

Use the distributive property to multiply \frac{1}{6} by 3x+4.

$$\frac{1}{5}x+1<\frac{1}{6}\times 3x+\frac{1}{6}\times 4$$

Multiply \frac{1}{6} and 3 to get \frac{3}{6}.

$$\frac{1}{5}x+1<\frac{3}{6}x+\frac{1}{6}\times 4$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{1}{5}x+1<\frac{1}{2}x+\frac{1}{6}\times 4$$

Multiply \frac{1}{6} and 4 to get \frac{4}{6}.

$$\frac{1}{5}x+1<\frac{1}{2}x+\frac{4}{6}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{1}{5}x+1<\frac{1}{2}x+\frac{2}{3}$$

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

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

Combine \frac{1}{5}x and -\frac{1}{2}x to get -\frac{3}{10}x.

$$-\frac{3}{10}x+1<\frac{2}{3}$$

Subtract 1 from both sides.

$$-\frac{3}{10}x<\frac{2}{3}-1$$

Convert 1 to fraction \frac{3}{3}.

$$-\frac{3}{10}x<\frac{2}{3}-\frac{3}{3}$$

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

$$-\frac{3}{10}x<\frac{2-3}{3}$$

Subtract 3 from 2 to get -1.

$$-\frac{3}{10}x<-\frac{1}{3}$$

Multiply both sides by -\frac{10}{3}, the reciprocal of -\frac{3}{10}. Since -\frac{3}{10} is negative, the inequality direction is changed.

$$x>-\frac{1}{3}\left(-\frac{10}{3}\right)$$

Multiply -\frac{1}{3} times -\frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$x>\frac{-\left(-10\right)}{3\times 3}$$

Do the multiplications in the fraction \frac{-\left(-10\right)}{3\times 3}.

$$x>\frac{10}{9}$$