Solve a+4/2+13-4a/5<0

$$\frac { a + 4 } { 2 } + \frac { 13 - 4 a } { 5 } < 0$$

Solve for a

$$a>\frac{46}{3}$$

Solution Steps

Multiply both sides of the equation by 10, the least common multiple of 2,5. Since 10 is positive, the inequality direction remains the same.

$$5\left(a+4\right)+2\left(13-4a\right)<0$$

Use the distributive property to multiply 5 by a+4.

$$5a+20+2\left(13-4a\right)<0$$

Use the distributive property to multiply 2 by 13-4a.

$$5a+20+26-8a<0$$

Add 20 and 26 to get 46.

$$5a+46-8a<0$$

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

$$-3a+46<0$$

Subtract 46 from both sides. Anything subtracted from zero gives its negation.

$$-3a<-46$$

Divide both sides by -3. Since -3 is negative, the inequality direction is changed.

$$a>\frac{-46}{-3}$$

Fraction \frac{-46}{-3} can be simplified to \frac{46}{3} by removing the negative sign from both the numerator and the denominator.

$$a>\frac{46}{3}$$