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.