Solve 2x+2+3x-1/5/5<10x+1/3

$$\frac{ 2x+2+ \frac{ 3x-1 }{ 5 } }{ 5 } < \frac{ 10x+1 }{ 3 }$$

Solve for x

$$x>\frac{2}{211}$$

Solution Steps

Multiply both sides of the equation by 15, the least common multiple of 5,3. Since 15 is positive, the inequality direction remains the same.

$$3\left(2x+2+\frac{3x-1}{5}\right)<5\left(10x+1\right)$$

Use the distributive property to multiply 3 by 2x+2+\frac{3x-1}{5}.

$$6x+6+3\times \frac{3x-1}{5}<5\left(10x+1\right)$$

Express 3\times \frac{3x-1}{5} as a single fraction.

$$6x+6+\frac{3\left(3x-1\right)}{5}<5\left(10x+1\right)$$

Use the distributive property to multiply 3 by 3x-1.

$$6x+6+\frac{9x-3}{5}<5\left(10x+1\right)$$

Use the distributive property to multiply 5 by 10x+1.

$$6x+6+\frac{9x-3}{5}<50x+5$$

Divide each term of 9x-3 by 5 to get \frac{9}{5}x-\frac{3}{5}.

$$6x+6+\frac{9}{5}x-\frac{3}{5}<50x+5$$

Combine 6x and \frac{9}{5}x to get \frac{39}{5}x.

$$\frac{39}{5}x+6-\frac{3}{5}<50x+5$$

Convert 6 to fraction \frac{30}{5}.

$$\frac{39}{5}x+\frac{30}{5}-\frac{3}{5}<50x+5$$

Since \frac{30}{5} and \frac{3}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{39}{5}x+\frac{30-3}{5}<50x+5$$

Subtract 3 from 30 to get 27.

$$\frac{39}{5}x+\frac{27}{5}<50x+5$$

Subtract 50x from both sides.

$$\frac{39}{5}x+\frac{27}{5}-50x<5$$

Combine \frac{39}{5}x and -50x to get -\frac{211}{5}x.

$$-\frac{211}{5}x+\frac{27}{5}<5$$

Subtract \frac{27}{5} from both sides.

$$-\frac{211}{5}x<5-\frac{27}{5}$$

Convert 5 to fraction \frac{25}{5}.

$$-\frac{211}{5}x<\frac{25}{5}-\frac{27}{5}$$

Since \frac{25}{5} and \frac{27}{5} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{211}{5}x<\frac{25-27}{5}$$

Subtract 27 from 25 to get -2.

$$-\frac{211}{5}x<-\frac{2}{5}$$

Multiply both sides by -\frac{5}{211}, the reciprocal of -\frac{211}{5}. Since -\frac{211}{5} is negative, the inequality direction is changed.

$$x>-\frac{2}{5}\left(-\frac{5}{211}\right)$$

Multiply -\frac{2}{5} times -\frac{5}{211} by multiplying numerator times numerator and denominator times denominator.

$$x>\frac{-2\left(-5\right)}{5\times 211}$$

Do the multiplications in the fraction \frac{-2\left(-5\right)}{5\times 211}.

$$x>\frac{10}{1055}$$

Reduce the fraction \frac{10}{1055} to lowest terms by extracting and canceling out 5.

$$x>\frac{2}{211}$$