Question

Identify the solution set of the inequality using the given replacement set.

x < –7; {–15, –10.5, –7.2, –7, 0, 6}

Answer 1

0 and 6 should be replaced. For x<-7, and 0 and 6 are greater than -7.

Answer 2

can u help me on like 3 more???

Answer 3

I think that -7 should be replaced too, for it is equal to -7, not smaller than it. Maybe it is
x≤−7
, not x<-7.

Answer 4

Solve.

4y + 16 > –8

Answer 5

First, let's work on the left hand side of your inequality, the 4y+16
This means, for instance, to see if it can be simplified at all.
Multiply y and 4

Multiply y and 1

The y just gets copied along.

The answer is y

y

4*y evaluates to 4y

4*y+16 evaluates to 4y+16

Answer 6

So, all-in-all, the left hand side of your inequality can be written as: 4y+16

Answer 7

okay

Answer 8

Now, let's work on the right hand side of your inequality, the -8
Because of the minus sign

8 becomes - 8

The answer is -8

The right hand side of your inequality can be written as: -8

Answer 9

So with these (any) simplifications, the inequality we'll set out to solve is:
4y+16 › -8

Move the 16 to the right hand side by subtracting 16 from both sides, like this:

From the left hand side:
16 - 16 = 0

The answer is 4y

From the right hand side:
-8 - 16 = -24

The answer is -24


Now, the inequality reads:
4y › -24
To isolate the y, we have to divide both sides of the inequality by the other "stuff" (variables or coefficients)
around the y on the left side of the inequality.

Answer 10

The last step is to divide both sides of the inequality by 4 like this:

To divide y by 1

The y just gets copied along in the numerator.

The answer is y

4y ÷ 4 = y

-24 ÷ 4 = -6

The solution to your inequality is:
y › -6

Answer 11

solve -r/4 < 8

Answer 12

First, let's work on the left hand side of your inequality, the -r/4
This means, for instance, to see if it can be simplified at all.
To divide r by 1

The r just gets copied along in the numerator.

The answer is r

r/4 evaluates to

Because of the minus sign

becomes -

The answer is

So, all-in-all, the left hand side of your inequality can be written as:
Now, let's work on the right hand side of your inequality, the 8
The right hand side of your inequality can be written as: 8 So with these (any) simplifications, the inequality we'll set out to solve is:
‹ 8


To isolate the r, we have to divide both sides of the inequality by the other "stuff" (variables or coefficients)
around the r on the left side of the inequality.
The last step is to divide both sides of the inequality by like this:

To divide r by 1

The r just gets copied along in the numerator.

The answer is r

÷ = r

8 ÷ = -32

Note! Here's an important point about inequalities:

We are now dividing by -0.25, which is a number less than zero! This changes the form of your inequality. Or, in other words, your ‹ will now become a ›.
The solution to your inequality is:
r › -32

So, your solution is:

r must be greater than -32

Answer 13

okay

Answer 14

and last how would this look on a number line -x/2<8