Question

Medal to whoever answers correctly! :)

Answer 1

yes.

Answer 2

-7z - 7 \[\le \] -5z + 5.

Answer 3

what kind of math was this?

Answer 4

like i know its algebra what kind of question. i forget.

Answer 5

you need isolate z

Answer 6

Graphing solution sets for inequalities.

Answer 7

okay after i got everything, this is what i got. z>=6

Answer 8

-7z - 7 -5z + 5.

First, let's work on the left hand side of your inequality, the -7z - 7
This means, for instance, to see if it can be simplified at all.
Multiply z and 7
Multiply z and 1


The z just gets copied along.

The answer is z

z

7*z evaluates to 7z

Because of the minus sign

7z becomes - 7z

The answer is -7z

-7*z-7 evaluates to -7z-7

So, all-in-all, the left hand side of your inequality can be written as: -7z-7

Now, let's work on the right hand side of your inequality, the -5z + 5.
Multiply z and 5
Multiply z and 1


The z just gets copied along.

The answer is z

z

5*z evaluates to 5z

Because of the minus sign

5z becomes - 5z

The answer is -5z

-5*z+5. evaluates to -5z+5

The right hand side of your inequality can be written as: -5z+5

So with these (any) simplifications, the inequality we'll set out to solve is:
-7z-7 -5z+5

Move the -7 to the right hand side by adding 7 to both sides, like this:
To the left hand side:
-7 + 7 = 0

The answer is -7z

To the right hand side:
5 + 7 = 12

The answer is 12-5z


Now, the inequality reads:
-7z 12-5z

Move the -5z to the left hand side by adding 5z to both sides, like this:
To the left hand side:
-7z + 5z = -2z

The answer is -2z

To the right hand side:
-5z + 5z = 0z

The answer is 12


Now, the inequality reads:
-2z 12
To isolate the z, we have to divide both sides of the inequality by the other "stuff" (variables or coefficients)
around the z on the left side of the inequality.

The last step is to divide both sides of the inequality by -2 like this:
To divide z by 1


The z just gets copied along in the numerator.

The answer is z

-2z ÷ -2 = z


12 ÷ -2 = -6

Answer 9

note that since we are dividing by a -2 it will change the direction of your inequality! So it went from <= to >=

Answer 10

Correct! z \[\ge \] -6.