Question

Solve the given inequality. Describe the solution set using the set-builder or interval notation. Then, graph the solution set on a number line.

4m +16.5 < 33.5

Answer 1

m < 4.25; (-∞, 4.25).

Explanation:

Part 1. Solve the inequality

4m + 16.5 < 33.5

4m < 17 Subtracted 16.5 from each side

m < 4.25 Divided each side by 4

Part 2. Interval notation

The solution set consists of all numbers less than 4.25. We use parentheses to denote numbers that are not included in the interval.

4.25 is not included, because m < 4.25.

-∞ is not included, because we can never reach it.

In interval notation, the solution set is (-∞, 4.25).

Step 3. Number line

The solution set consists of all numbers less than 4.25. We use an open circle to show that 4.25 is not included in the set.

Answer 2

solution (-∞,4.25)

Explanation:

Given inequality is
`4m +16.5 < 33.5`.

Now we need to solve the given inequality. Describe the solution set using the set-builder or interval notation. Then, graph the solution set on a number line.

`4m +16.5 < 33.5`

`4m < 33.5 - 16.5`

`4m < 17`

`m < (17)/(4)`

`m < 4.25`

Hence solution set using interval notation is given by (-∞,4.25).

Graph will be an arrow pointing to the left of 4.25