Question

Solve the following inequality and write your solution using set builder notation.

-6/25x is greater than or equal to -5/3

Answer 1

Given inequality is

-6/25x ≥ -5/3

Apply multiplication property, multiply 25x toeach side.

(-6/25X)25x ≥ (-5/3)25x

-6 >= -125x/3

Apply multiplication property, multiple by 3 to each side.

(-6)(3) ≥  (-125x/3)(3)

-18 ≥ -125x 

 -18/-125 ≥ x multiply with negative one and do not forget to change the inequality symbol

x ≥ 18/125

Set builder notation  {x belongs to R / x ≥ 18/125}

Comments

The solution set of the inequality is .

Answer 2

The inequality is .

Multiply each side by negative one and flip the symbol.

Product of two same signs is positive.

Apply multiplication property of inequality : Multiply each side by  25.

Cancel common terms.

Apply division property of inequality : Divide each side by  6.

Cancel common terms.

.

The solution set is .