Question

Question #2d8d7

Answer 1

`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`.