-1/3H < or equal to 7 how is it done?

I know signs need to be switched but
is there any reciprocating the fraction?

Urgent!!!! plz answer

If

-1/3 H < 7
just multiply by 3
-H < 7
now multiply by -1 and swap direction:
H > -7

If it's not clear why multiplying/dividing by a negative value changes direction, think of it as adding/subtracting on both sides:

-H < 7
-H + H < 7 + H
0 < 7+H
0-7 < 7+H-7
-7 < H

multiplying by a negative value is just a shorthand way of moving things from one side to the other.

To solve the inequality -1/3H ≤ 7, you're correct that you need to switch the direction of the inequality sign because you're multiplying or dividing by a negative (-1/3).

To isolate the variable H, you can start by multiplying both sides of the inequality by -3 which is the reciprocal of -1/3. However, because we multiply by a negative number, we also need to flip the inequality sign:

(-1/3H)(-3) ≥ 7(-3)
H ≥ -21

So the solution to the inequality is H ≥ -21.

To recap:
1. Flip the inequality sign: ≤ becomes ≥.
2. Multiply both sides by the reciprocal of the coefficient (-1/3) to isolate the variable.
3. Simplify and solve for H.

In this case, reciprocating the fraction involved multiplying by the reciprocal (-3). But remember, when you multiply or divide by a negative number, the inequality sign must be flipped.