Question

Graph the solution to the inequality on the number line.10-31 =7HHHHHHHHHHHHHHHHHHHHH-11-10 -9 -8 -7 -6 -5 4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11

Answer 1

Given the inequality:

`|v-3|\leq7`

Then:

`\begin{gathered} v-3\leq7,v-3\ge0 \\ \\ -(v-3)\leq7,v-3<0 \end{gathered}`

Solving the inequalities:

`\begin{gathered} v\leq10,v\ge3 \\ \\ v\ge-4,v<3 \end{gathered}`

Finding the intersection:

`[3,10]`
`[-4,3)`

Finally, we find the union between both results:

`[-4,10]`

ANSWER