Solve -1/5x+2+13/4>33/5

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

Solve for x

$$x<\frac{3}{4}$$

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.

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

Multiply 1 and 4 to get 4.

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

Add 4 and 3 to get 7.

$$-4x+40+5\times 7>4\left(3\times 5+3\right)$$

Multiply 5 and 7 to get 35.

$$-4x+40+35>4\left(3\times 5+3\right)$$

Add 40 and 35 to get 75.

$$-4x+75>4\left(3\times 5+3\right)$$

Multiply 3 and 5 to get 15.

$$-4x+75>4\left(15+3\right)$$

Add 15 and 3 to get 18.

$$-4x+75>4\times 18$$

Multiply 4 and 18 to get 72.

$$-4x+75>72$$

Subtract 75 from both sides.

$$-4x>72-75$$

Subtract 75 from 72 to get -3.

$$-4x>-3$$

Divide both sides by -4. Since -4 is negative, the inequality direction is changed.

$$x<\frac{-3}{-4}$$

Fraction \frac{-3}{-4} can be simplified to \frac{3}{4} by removing the negative sign from both the numerator and the denominator.

$$x<\frac{3}{4}$$