Question #2d8d7

1 Answer
sente
Oct 28, 2016

#3# is the least number satisfying the given conditions.

Explanation:

Let #x# represent the number in question. The expression "#5# times a number is increased by #4#" can then be represented by #5x+4#. We are given that that expression is at least #19#, meaning it is greater than or equal to #19#. Putting the entire inequality in algebraic terms, then, we have

#5x+4 >= 19#

We can add or subtract any real number from both sides of an inequality without changing the inequality.

#=> 5x + 4 - 4 >= 19-4#

#=> 5x >= 15#

Similarly, we can divide by a positive number without changing the inequality (dividing by a negative number would require us to switch the direction of the inequality).

#=> (5x)/5 >= 15/5#

#:. x >= 3#

The least number satisfying #x>=3# is #3#.

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