Chapter 3.5, Problem 13PPE

To determine

The solution of given inequality in set-builder notation.

Answer to Problem 13PPE

The set-builder notation, the solution is $\{y\mid y\ge 4\}$

Explanation of Solution

Given information:

The inequality,

  $4y+7\ge 23$

Calculation:

Consider the inequality,

  $4y+7\ge 23$ .

To solve the inequality, move all the constants to the right and keep variable in the left.

The inequality can be solved as follows:

  $4y+7\ge 23$ Consider the original inequality

  $4y+1-1\ge 25-1$ Subtract each side by 7

  $4y\ge 16$ Simplify

  $\frac{4y}{4}\ge \frac{16}{4}$ Divide each side by 4

  $y\ge 4$ Simplify

Therefore, the solution is $y\ge 4$ .

The set builder form describes a properties of an element must have to be included in a set.

In set-builder notation, the solution is $\{y\mid y\ge 4\}$ .