Solve Each innequality

Question

(3x+5)(4x-8)>0

Answer 1

(3x + 5)(4x - 8) > 0

Either both factors are positive or both factors are negative

3x + 5 > 0 and 4x - 8 > 0

3x > -5 and 4x > 8

x > -5 /3 and x > 2

x > 2

or

3x + 5 < 0 and 4x - 8 < 0

3x < -5 and 4x < 8

x < -5 / 3 and 4x < 2

x < -5 / 3

Answer 2

Here we can use the zero product property to solve this equation. It means when the product of two polynomials is equal to zero, you can put each polynomial equal to zero and solve them individually.

For our example, we can split this problem into

3x+5 > 0 and 4x-8> 0

Then you can solve each inequality like normal.

x > -5/3 and x > 2