# Question #2d8d7

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 $5 x + 4$. 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

$5 x + 4 \ge 19$

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

$\implies 5 x + 4 - 4 \ge 19 - 4$

$\implies 5 x \ge 15$

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).

$\implies \frac{5 x}{5} \ge \frac{15}{5}$

$\therefore x \ge 3$

The least number satisfying $x \ge 3$ is $3$.