Solve -1/2+5(x+1)>2(1/53+x)+1/2

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

Solve for x

$$x>-\frac{14}{15}$$

Solution Steps

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

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

Convert 5 to fraction \frac{10}{2}.

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

Since -\frac{1}{2} and \frac{10}{2} have the same denominator, add them by adding their numerators.

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

Add -1 and 10 to get 9.

$$\frac{9}{2}+5x>2\left(\frac{1}{5}\times 3+x\right)+\frac{1}{2}$$

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

$$\frac{9}{2}+5x>2\left(\frac{3}{5}+x\right)+\frac{1}{2}$$

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

$$\frac{9}{2}+5x>2\times \frac{3}{5}+2x+\frac{1}{2}$$

Express 2\times \frac{3}{5} as a single fraction.

$$\frac{9}{2}+5x>\frac{2\times 3}{5}+2x+\frac{1}{2}$$

Multiply 2 and 3 to get 6.

$$\frac{9}{2}+5x>\frac{6}{5}+2x+\frac{1}{2}$$

Least common multiple of 5 and 2 is 10. Convert \frac{6}{5} and \frac{1}{2} to fractions with denominator 10.

$$\frac{9}{2}+5x>\frac{12}{10}+2x+\frac{5}{10}$$

Since \frac{12}{10} and \frac{5}{10} have the same denominator, add them by adding their numerators.

$$\frac{9}{2}+5x>\frac{12+5}{10}+2x$$

Add 12 and 5 to get 17.

$$\frac{9}{2}+5x>\frac{17}{10}+2x$$

Subtract 2x from both sides.

$$\frac{9}{2}+5x-2x>\frac{17}{10}$$

Combine 5x and -2x to get 3x.

$$\frac{9}{2}+3x>\frac{17}{10}$$

Subtract \frac{9}{2} from both sides.

$$3x>\frac{17}{10}-\frac{9}{2}$$

Least common multiple of 10 and 2 is 10. Convert \frac{17}{10} and \frac{9}{2} to fractions with denominator 10.

$$3x>\frac{17}{10}-\frac{45}{10}$$

Since \frac{17}{10} and \frac{45}{10} have the same denominator, subtract them by subtracting their numerators.

$$3x>\frac{17-45}{10}$$

Subtract 45 from 17 to get -28.

$$3x>\frac{-28}{10}$$

Reduce the fraction \frac{-28}{10} to lowest terms by extracting and canceling out 2.

$$3x>-\frac{14}{5}$$

Divide both sides by 3. Since 3 is positive, the inequality direction remains the same.

$$x>\frac{-\frac{14}{5}}{3}$$

Express \frac{-\frac{14}{5}}{3} as a single fraction.

$$x>\frac{-14}{5\times 3}$$

Multiply 5 and 3 to get 15.

$$x>\frac{-14}{15}$$

Fraction \frac{-14}{15} can be rewritten as -\frac{14}{15} by extracting the negative sign.

$$x>-\frac{14}{15}$$