# How do you solve and graph #v+8<3# or #-8v< -40#?

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To solve the compound inequality ( v + 8 < 3 ) or ( -8v < -40 ), follow these steps:

- Solve each inequality separately.
- Graph the solutions on a number line.
- Identify the intersection of the solutions, if any.

For the first inequality ( v + 8 < 3 ):

( v + 8 < 3 ) ( v < 3 - 8 ) ( v < -5 )

For the second inequality ( -8v < -40 ):

( -8v < -40 ) To solve for v, divide both sides by -8, remembering to reverse the inequality sign: ( v > \frac{{-40}}{{-8}} ) ( v > 5 )

Now, graph the solutions on a number line:

For ( v < -5 ), draw an open circle at -5 (since it's not included in the solution) and shade to the left.

For ( v > 5 ), draw an open circle at 5 (since it's not included in the solution) and shade to the right.

The combined solution is the union of the individual solutions. So, the graph shows the shaded regions to the left of -5 and to the right of 5 on the number line.

The final graph visually represents the solution to the compound inequality ( v + 8 < 3 ) or ( -8v < -40 ).

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