Solve 1+x+3/5>1-x

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

Solve for x

$$x>-\frac{1}{2}$$

Solution Steps

Multiply both sides of the equation by 5. Since 5 is positive, the inequality direction remains the same.

$$5+x+3>5-5x$$

Add 5 and 3 to get 8.

$$8+x>5-5x$$

Add 5x to both sides.

$$8+x+5x>5$$

Combine x and 5x to get 6x.

$$8+6x>5$$

Subtract 8 from both sides.

$$6x>5-8$$

Subtract 8 from 5 to get -3.

$$6x>-3$$

Divide both sides by 6. Since 6 is positive, the inequality direction remains the same.

$$x>\frac{-3}{6}$$

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

$$x>-\frac{1}{2}$$