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

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

Solve for x

$$x<\frac{27}{4}$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 2,3. Since 6 is positive, the inequality direction remains the same.

$$-30<3\left(-1\right)-2\times 2x$$

Multiply 3 and -1 to get -3. Multiply -2 and 2 to get -4.

$$-30<-3-4x$$

Swap sides so that all variable terms are on the left hand side. This changes the sign direction.

$$-3-4x>-30$$

Add 3 to both sides.

$$-4x>-30+3$$

Add -30 and 3 to get -27.

$$-4x>-27$$

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

$$x<\frac{-27}{-4}$$

Fraction \frac{-27}{-4} can be simplified to \frac{27}{4} by removing the negative sign from both the numerator and the denominator.

$$x<\frac{27}{4}$$