2/5(x-3) < 4-2/5(3-2x) <= 7x-2/5(x-3)

Question

I dont know how to solve this inequality, please help me

Answer 1

We can break up the inequality into two parts.

 

(2/5)(x - 3) < 4 - (2/5)(3 - 2x)       and       4 - (2/5)(3 - 2x) ≤ 7x -(2/5)(x - 3)

 

This gives us a clue that we will have two solutions in the inequality.  Let's work with the first part.

 

 

(2/5)(x - 3) < 4 - (2/5)(3 - 2x)    

 

 

Distribute the terms to get rid of parentheses, making it easier to deal with the inequality.

 

(2/5)x - (6/5) < 4 - (6/5) + (4/5)x

 

 

Let's get the fractions to have common denominators.  The common denominator is 5.

 

(2x - 6) / 5 < (20 - 6 + 4x) / 5

 

 

The denominators on both sides of equation are equal to each other.  We only need to compare the numerators.

 

2x - 6 < 14 + 4x

 

 

Subtract 2x on both sides of equation.

 

-6 < 14 + 2x

 

 

Subtract 14 on both sides of equation.

 

-20 < 2x

 

-10 < x

 

x > -10

 

This is one solution of the inequality.  Now that you know how to tackle this problem, try the other part to find the other solution.