Question 100726
Let x represent 1 less than the total number of minutes for a long-distance phone call. The total cost of the call is 36 cents ($0.36) for the first minute plus 21 cents ($0.21) for each additional minute. So, the number of minutes that cost .36 is 1, by definition. And the total minutes at .21 = x.  (Remember, x is one less than the total number of minutes: you're charged .36 for the first minute, so you don't want to pay for it twice by including it in x.)

Given you want the call to cost less than $3, the inequality is:

{{{.36 + .21x < 3}}}.

Solving the inequality is needed to check the solution. Begin with the equivalent equation:

{{{.36 + .21x = 3}}}

Multiply through by 100 to remove the decimals, which makes the work easier.

{{{36 + 21x = 300}}}

Subtracting 36 from both sides, we have:

{{{21x = 264}}}

Dividing both sides by 21, we have:

{{{x = 264/21 = 12.57}}}.

Returning to the inequality, when {{{x < 12.57}}}, the total cost of the long-distance call will be less than $3.

Check by substituting.

{{{.36 + .21(12.57) < 3}}}, which equals 2.9997. Check.

Keep in mind that if asked how long you could talk, you would have to add back the first minute. So x+1 = 13.57, which is how long the phone call could be and still cost less than $3.