Question

Given: 5x+3> 4x+7 Choose the graph of the solution set

Answer 1

x > 4 is a solution to the given inequality.

Explanation:

We are given an inequality in the question.

`5x+3> 4x+7`

We have to graph this inequality.

In order to graph this inequality, we first solve the inequality.

Solution to inequality:

`5x+3> 4x+7\\5x>4x + 7-3\\5x>4x+4\\5x-4x>4\\x>4`

In interval form we can write the solution as:

`x \in (4, \infty)`

The attached image shows the graph for the given inequality.

The dotted line on the graph shows that the points on the line does not belong to the solution set.

All the points in the red shaded region is a solution he given inequality.

Answer 2

First solve the inequality to determine the solution set. Solving the inequality we have

`5x+3>4x+7`

`5x-4x>7-3`

`x>4`

Then, the solution set is
`\{x\in \mathbb{R}\lvert x>4\}=(4,\infty)`. The solution is the interval
`(4,\infty)` and it can be represented by the following graph.

Explanation: