Question

Write the solution in interval notation: 4v+2>-2 or 3v-5<7

Answer 1

For this case we must find the solution of the following inequalities:

$4v + 2> -2\ or\ 3v-5$

From the first inequality we have:

$4v + 2> -2$

Subtracting 2 from both sides of the inequality:

$4v> -2-2$

Equal signs are added and the same sign is placed.

$4v> -4$

Dividing between 4 on both sides of the inequality:

$v> \frac {-4} {4}\\v> -1$

Thus, the solution is given by all values of "v" greater than -1.

From the second inequality we have:

$3v-5$

Adding 5 to both sides of the inequality we have:

$3v$

Dividing by 3 to both sides of the inequality we have:

$v$

Thus, the solution is given by all values of "v" less than 4.

Then, the solution set is given by the union of both intervals.

The union consists of all the elements that are contained in each interval.

(-∞,∞)

Answer:

The solution set is: (-∞,∞)