Hello, Please check my answers, with stars (*) are my answers! Please check if they are wrong please tell the right answer and why it is right (explain it) so I can understand why! Thanks!

For questions 1-2, solve the inequality.

1.) x + 8 < -28

a~ x < -36 ******
b~ x < -20
c~ x < 20
d~ x < 36

2.) -3p > -48

a~ p < 16 *******
b~ p > -51
c~ p < -16
d~ p > 16

3.) Describe the number of solutions for the equation.
5(x-9)= 5x

a~ one solutions ********
b~ no solutions
c~ infinite solutions

4.) Describe the number of solutions for the equation.
-3(x-5)= 3x + 9

a~ one solutions ********
b~ no solutions
c~ infinite solutions

Solve the inequality.

5.) 9x < 72

a~ x < 8
b~ x < -8
c~ x < 63 ******
d~ x < 81

3B how can you have 5x-45 = 5x?

5A divide by 9, not subtract

The others are ok

OK I understood, Thnx for answering fast!

Let's check your answers step-by-step:

1.) x + 8 < -28

To solve this inequality, we need to isolate the variable x.

Subtract 8 from both sides of the inequality:

x < -28 - 8

x < -36

Your answer, x < -36, is correct. Well done!

2.) -3p > -48

To solve this inequality, we need to isolate the variable p.

Divide both sides of the inequality by -3. Since we are dividing by a negative number, the inequality sign will flip direction:

p < -48 / -3

p < 16

Your answer, p < 16, is correct. Great job!

3.) 5(x-9) = 5x

To determine the number of solutions for this equation, we will simplify and evaluate it.

5(x-9) can be simplified to 5x - 45.

So the equation becomes 5x - 45 = 5x.

Now, subtracting 5x from both sides will result in -45 = 0.

Since -45 is not equal to 0, there are no solutions to this equation.

Your answer, "no solutions," is incorrect. The correct answer is "infinite solutions" because any value of x will satisfy the equation since both sides are equal.

4.) -3(x-5) = 3x + 9

Similar to the previous question, we need to simplify and evaluate this equation.

Expanding -3(x-5) gives us -3x + 15.

So the equation becomes -3x + 15 = 3x + 9.

Next, we want to isolate the variable x, so let's move all the terms with x to one side of the equation and the constant terms to the other side.

Adding 3x to both sides gives us 15 = 6x + 9.

Subtracting 9 from both sides gives us 6 = 6x.

Dividing both sides by 6 gives us x = 1.

Therefore, there is one solution to this equation.

Your answer, "one solution," is correct. Good job!

5.) 9x < 72

To solve this inequality, we need to isolate the variable x.

Divide both sides of the inequality by 9:

9x / 9 < 72 / 9

x < 8

Your answer, x < 8, is incorrect. The correct answer is x < 63.

Dividing both sides of the inequality by 9 gives us x < 8.

Therefore, the correct answer is c~ x < 63.

I hope this helps clarify the correct answers and why they are right. Let me know if you have any more questions!

1.) The correct answer is b~ x < -20.

To solve the inequality x + 8 < -28, we need to isolate x on one side of the inequality sign.

x + 8 < -28

Subtract 8 from both sides:

x < -28 - 8

x < -36

So the correct answer is option b~ x < -20.

2.) The correct answer is a~ p < 16.

To solve the inequality -3p > -48, we need to isolate p on one side of the inequality sign.

-3p > -48

Divide by -3 (since we are dividing by a negative number, the inequality sign flips):

p < -48 / -3

p < 16

So the correct answer is option a~ p < 16.

3.) The correct answer is a~ one solution.

For the equation 5(x-9) = 5x, we can simplify and solve for x:

5x - 45 = 5x

Subtract 5x from both sides:

-45 = 0

This is a contradiction. It means that the equation is inconsistent and has no solution.

So the correct answer is b~ no solutions.

4.) The correct answer is b~ no solutions.

For the equation -3(x-5) = 3x + 9, we can simplify and solve for x:

-3x + 15 = 3x + 9

Subtract 3x from both sides:

15 = 6x + 9

Subtract 9 from both sides:

6 = 6x

Divide by 6:

1 = x

But if you substitute x = 1 back into the equation, you'll find it doesn't satisfy the equation:

-3(1-5) = 3(1) + 9

-3(-4) = 3 + 9

12 = 12

This is a true statement and again means that the equation is inconsistent and has no solution.

So the correct answer is b~ no solutions.

5.) The correct answer is c~ x < 63.

To solve the inequality 9x < 72, we need to isolate x on one side of the inequality sign.

9x < 72

Divide by 9:

x < 72 / 9

x < 8

So the correct answer is option c~ x < 63.