Solve the inequality : (3/5) + b >= 2/3

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given the inequality:

3/5  + b >= 2/3

Let us isolate b on the left side.

Then we will subtract 3/5 from both sides.

==> b >= 2/3 - 3/5

==> b >= (10 - 9) /15

==> b >= 1/15

Then the values of b must be equal of greater than 1/15 in order for the inequality to hold.

Then the solution is b = [ 1/15 , inf)

tonys538's profile pic

tonys538 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

In the case of an inequality it is possible to add and subtract the same value without altering the inequality. Both the sides can also be multiplied or divided by the same positive number. Multiplying or dividing the sides by a negative number inverts the sign of the inequality.

To solve `(3/5) + b >= 2/3` , subtract 3/5 from both the sides.

`(3/5) + b - 3/5 >= 2/3 - 3/5`

`b >= 1/15`

The solution of the inequality is b can take on all values greater than or equal to 1/15

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll keep the unknown b to the left side and we'll move the number alone to the right side:

b >= 2/3 - 3/5

We'll calculate the LCD of the fractions from the right side:

b >= 5*2/15 - 3*3/15

b >= 10/15 - 9/15

b >= 1/15

The interval of possible values for b is: [1/15 ; +infinite).

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