Question

Which points would you find on the graph for |x|+3>7?

Answer 1

-7 and 5

Step-by-step explanation:
`|x|\text{ + 3 > 7}`

To find the points without a graph, we will substittute x with the values in each of the options.

If the expression of the left hand side and right hand side is correct, then it will be on the graph.

`\begin{gathered} |x|\text{ + 3> 7} \\ \text{for x = 7} \\ |7|\text{ + 3 > 7} \\ 7\text{ + 3 > 7} \\ 10\text{ > 7 (correct)} \end{gathered}`
`\begin{gathered} \text{for x = -5} \\ |-5|\text{ + 3 > 7} \\ 5\text{ }+\text{ 3 > 7} \\ 8\text{ > 7 (correct)} \end{gathered}`
`\begin{gathered} \text{for x = -4} \\ |-4|\text{ + 3 > 7} \\ 4\text{ + 3 > 7} \\ 7\text{ > 7 (wrong)} \end{gathered}`
`\begin{gathered} \text{for x = 2} \\ |2|\text{ + 3 > 7} \\ 2\text{ + 3 > 7} \\ 5\text{ > 7 (wrong)} \end{gathered}`

Using a graph:

From the graph, 7 and -5 are on the graph

-4 is on the dashed line so we can't say it is on the graph. The dashed line shows the number is not included.