Solve 2x-5<7/2x-1

$$2 x - 5 < \frac { 7 } { 2 } x - 1$$

Solve for x

$$x>-\frac{8}{3}$$

Solution Steps

Subtract \frac{7}{2}x from both sides.

$$2x-5-\frac{7}{2}x<-1$$

Combine 2x and -\frac{7}{2}x to get -\frac{3}{2}x.

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

Add 5 to both sides.

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

Add -1 and 5 to get 4.

$$-\frac{3}{2}x<4$$

Multiply both sides by -\frac{2}{3}, the reciprocal of -\frac{3}{2}. Since -\frac{3}{2} is negative, the inequality direction is changed.

$$x>4\left(-\frac{2}{3}\right)$$

Express 4\left(-\frac{2}{3}\right) as a single fraction.

$$x>\frac{4\left(-2\right)}{3}$$

Multiply 4 and -2 to get -8.

$$x>\frac{-8}{3}$$

Fraction \frac{-8}{3} can be rewritten as -\frac{8}{3} by extracting the negative sign.

$$x>-\frac{8}{3}$$