5. A student solved the following equation using the following steps:
2(2x+2)=4(x+4)
4x+4=4x+4
4=4
Infinitely many solutions
(2 points)
Based on the student's work, the equation was solved
incorrectly
The equation solved correctly would show that it has
one
solution(s). true or false
False
how many solutions does the equation have
The equation has infinitely many solutions.
that is not a answer choice
Apologies for the confusion. The equation has one solution.
7. Which equation has the same first step to solve as this equation: 2x+12−3x=27
(1 point)
Responses
4x−17+2x=9
4 x minus 17 plus 2 x is equal to 9
2x+12=27
2 x plus 12 is equal to 27
2x+12=−3x−27
2 x plus 12 is equal to negative 3 x minus 27
2(x−5)+2x=10
2x + 12 = 27
11. After combining like terms to simplify the equation 3−15x+24+16x=4x−24−4x
, what would be the next best step to finish solving?(1 point)
Responses
Subtract 27 from both sides of the equation.
Subtract 27 from both sides of the equation.
Subtract 24 from both sides of the equation.
Subtract 24 from both sides of the equation.
Subtract x from both sides of the equation.
Subtract x from both sides of the equation.
Add x to both sides of the equation.
Add x to both sides of the equation.
Divide both sides of the equation by 15.
The next best step to finish solving the equation would be to subtract 24 from both sides of the equation.
check your answer bru
Apologies for the incorrect response. The correct next step to finish solving the equation 3 - 15x + 24 + 16x = 4x - 24 - 4x would be to combine like terms on both sides of the equation:
3 - 15x + 24 + 16x = 4x - 24 - 4x
27 + x = -24
Then, to isolate the variable, -24 needs to be subtracted from both sides of the equation:
27 + x - 24 = -24 - 24
x + 3 = -48
Therefore, the correct next step would be to subtract 24 from both sides of the equation.
12. Which inequality represents the graph below:
(1 point)
Responses
−3x−7≥−10
negative 3 x minus 7 is greater than or equal to negative 10
−3x+7<10
−3x+7<10
3x−7≤−10
3 x minus 7 is less than or equal to negative 10
3x+7>10
3x + 7 > 10
13. The speed limit sign on the expressway says that the speed limit is 55 mph. Write an inequality that represents all speeds you can legally drive on the expressway. (1 point)
Responses
x<55
x<55
x≤55
x is less than or equal to 55
x≥55
x is greater than or equal to 55
x>55
x ≤ 55
14. If you were to graph the inequality 35<7x
on a number line:(2 points)
Would you use an open or closed circle?
You would use an open circle at the point 35 on the number line.
Would your arrow on the number line point to the left or to the right?
The arrow on the number line would point to the right.
-5(x+5)>-15
To solve the inequality -5(x+5) > -15, first distribute the -5:
-5x - 25 > -15
Next, add 25 to both sides to isolate the variable:
-5x - 25 + 25 > -15 + 25
-5x > 10
Finally, divide both sides by -5, remembering to flip the inequality sign when dividing by a negative number:
-5x / -5 < 10 / -5
x < -2
Therefore, the solution to the inequality is x < -2.
5. Match the inequality to its graphed solution.(2 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
The option "negative 3 times open paren x minus 12 close paren is greater than 0" (4 of 4) has been selected. Press tab to choose a response area, and spacebar to insert it. Press escape to cancel.
Apologies, but I cannot see the available response options. Please provide the options for me to assist you further.
-5(x+5)>-15 and 8x<4x+28 and 1/4(8x+16)>-4 and -3(x-12)>0
Without the graphed solutions or available options to match with the inequalities, I cannot directly provide the correct matches. However, I can still help you solve each inequality:
1. -5(x+5) > -15
- Distribute the -5: -5x - 25 > -15
- Add 25 to both sides: -5x > 10
- Divide by -5 (and flip the inequality sign): x < -2
2. 8x < 4x + 28
- Subtract 4x from both sides: 4x < 28
- Divide by 4: x < 7
3. (1/4)(8x+16) > -4
- Multiply both sides by 4 to eliminate the fraction: 8x + 16 > -16
- Subtract 16 from both sides: 8x > -32
- Divide by 8: x > -4
4. -3(x-12) > 0
- Distribute the -3: -3x + 36 > 0
- Subtract 36 from both sides: -3x > -36
- Divide by -3 (and flip the inequality sign): x < 12
I apologize for the inconvenience caused by not being able to match these inequalities with their graphed solutions.
Question 11
16. You originally have x colored pencils in your pencil box. You share them equally between you and your friend. You add in 3 more colored pencils to your own box after sharing them. This gives you a total of 15 pencils.
a. Write an equation and show all of your steps for solving x (the original number of colored pencils in your box).
b. If you wanted to have at least 20 colored pencils left in your box, how many colored pencils would you have needed originally?
c. Write an inequality and show all steps for solving for x.
(5 points)
a. To solve for x, the original number of colored pencils in your box, we can set up the equation:
(x/2) + 3 = 15
Here, the (x/2) represents the number of colored pencils you have after sharing equally with your friend (since you both get half), and adding 3 represents the additional colored pencils you kept for yourself. The sum is equal to the total of 15 colored pencils.
Let's solve the equation step by step:
(x/2) + 3 = 15
Subtract 3 from both sides:
(x/2) = 15 - 3
(x/2) = 12
Multiply both sides by 2 to get rid of the fraction:
2 * (x/2) = 2 * 12
x = 24
Therefore, the original number of colored pencils in your box was 24.
b. To find out how many colored pencils you would have needed originally to have at least 20 left, we can set up another equation:
x - (x/2) + 3 ≥ 20
Here, (x/2) represents the number of colored pencils shared with your friend, and adding 3 represents the additional pencils you kept. We want this total to be greater than or equal to the desired 20 colored pencils left.
Let's solve the inequality step by step:
x - (x/2) + 3 ≥ 20
Multiply both sides by 2 to get rid of the fraction:
2 * (x - (x/2) + 3) ≥ 2 * 20
2x - x + 6 ≥ 40
Combine like terms:
x + 6 ≥ 40
Subtract 6 from both sides:
x ≥ 40 - 6
x ≥ 34
Therefore, you would have needed at least 34 colored pencils in your box originally to have at least 20 left.
c. The inequality representing having at least 20 colored pencils left can be written as:
x - (x/2) + 3 ≥ 20
In this inequality, (x/2) represents the number of colored pencils shared with your friend, and adding 3 represents the additional pencils you kept. We want this total to be greater than or equal to the desired 20 colored pencils left.
Please note that the inequality is the same as in part b, as we are solving for the same condition.
10. Jill solves the equation 3(x−5)+2x=0
. Fill in the blanks for each step with the correct values:(3 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
3x+
+2x=0
5x=
Response area
x=
To solve the equation 3(x - 5) + 2x = 0, let's fill in the blanks with the correct values:
3x + ___ + 2x = 0
5x + ___ = 0
___ = 0
First, distribute the 3:
3x - 15 + 2x = 0
Combine like terms:
5x - 15 = 0
Add 15 to both sides:
5x = 15
Now, solve for x:
x = 15/5
x = 3
So, the filled-in values are:
3x + (5 - 15) + 2x = 0
5x - 15 = 0
x = 3