Solve inequality. Check. then tell whether the given value is in the solution set

Question

-28 < m-14

 

is -10 a solution

 

 

45 > 15 + j

is 30 a solution

 

 

7> fraction f/4

is 32 a solution

 

 

 

 

 

Answer 1

Inequalities are solved using the same methods as equalities.  You can manipulate them the same way. So:

-28 ≤ m - 14

Add 14 to both sides:

-28 + 14 ≤ m 

-14 ≤ m

-10 is a solution, because m is greater than or equal to -14, so the solution set is written from -14 inclusive to positive infinity.  Written in interval form, this looks like: {-14,∞).  Written like your form: -14, -13, -12, -11, -10, -9.......,∞

Is -10 a solution, yes.

 

45 ≥ 15 + j

Subtract 15 from both sides:

45 - 15 ≥ j

30 ≥ j

30 is a solution, because j is less than or equal to 30, so the solution set is from negative infinity to 30 inclusive.  Interval form : (-∞, 30}.  Written like your form: -∞........,27, 28, 29, 30}.  Is 30 a solution, yes.

 

 

7 ≥ f/4

Multiply both sides by 4:

7 * 4 ≥ f

28 ≥ f

32 is not a solution, because f is less than or equal to 28, so the solution set is from negative infinity to 28 inclusive.  Interval form : (-∞, 28}.  Written like your form: -∞......, 26, 27, 28}.  Is 32 a solution, no.