Solve 2x+3/5-2>x+1/4

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

Solve for x

$$x>11$$

Solution Steps

Multiply both sides of the equation by 20, the least common multiple of 5,4. Since 20 is positive, the inequality direction remains the same.

$$4\left(2x+3\right)-40>5\left(x+1\right)$$

Use the distributive property to multiply 4 by 2x+3.

$$8x+12-40>5\left(x+1\right)$$

Subtract 40 from 12 to get -28.

$$8x-28>5\left(x+1\right)$$

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

$$8x-28>5x+5$$

Subtract 5x from both sides.

$$8x-28-5x>5$$

Combine 8x and -5x to get 3x.

$$3x-28>5$$

Add 28 to both sides.

$$3x>5+28$$

Add 5 and 28 to get 33.

$$3x>33$$

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

$$x>\frac{33}{3}$$

Divide 33 by 3 to get 11.

$$x>11$$