Jill solves the equation 3(x−5)+2x=0
. Fill in the blanks 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+
Response area +2x=0
5x=
Response area
x=
Response area
3x+10x=0
13x=0
x=0
Jill solves the equation 3(x−5)+2x=0
. Fill in the blanks 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+
Response area +2x=0
5x=
Response area
x=
Response area
3x - 15 + 2x = 0
5x - 15 = 0
x = 3
are you sure?
Apologies for the mistake. Let's solve the equation correctly:
3(x - 5) + 2x = 0
Distribute the 3:
3x - 15 + 2x = 0
Combine like terms:
5x - 15 = 0
Add 15 to both sides:
5x = 15
Divide both sides by 5:
x = 3
So the correct solution is x = 3.
Solve the equation by filling in the steps: 2(x−3)+21=−3
(4 points)
Step 1: Distribute to get
Step 2: Combine like terms to get
Step 3: Use
to get 2x=−18
Step 4: Use
to get x=−9
Step 1: Distribute to get 2x - 6 + 21 = -3
Step 2: Combine like terms to get 2x + 15 = -3
Step 3: Subtract 15 from both sides to get 2x = -18
Step 4: Divide both sides by 2 to get x = -9
Look at the steps for solving the equation and choose a true statement.
3x−9x+1=2(−3x+1)−1
−6x+1=−6x+2−1
−6x+1=−6x+1
(1 point)
Responses
The only solution to the equation is -6.
The only solution to the equation is -6.
The only solution to the equation is 1.
The only solution to the equation is 1.
There is no way to know if there is a solution to the equation.
There is no way to know if there is a solution to the equation.
There are infinitely many solutions to the equation.
There are infinitely many solutions to the equation.
There is no solution to the equation.
There is no solution to the equation.
The true statement is: There are infinitely many solutions to the equation.
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 x from both sides of the equation.
Subtract x from both sides of the equation.
Subtract 24 from both sides of the equation.
Subtract 24 from both sides of the equation.
Subtract 27 from both sides of the equation.
Subtract 27 from both sides of the equation.
Add 24 to both sides of the equation.
Add 24 to both sides of the equation.
Divide both sides of the equation by 15.
Divide both sides of the equation by 15.
Add x to both sides of the equation.
The next best step to finish solving would be: Add x to both sides of the equation.
A student solved the following equation using the following steps:
4(2−3x)=x−2(2x+1)
8−3x=x−4x−2
8−3x=−3x−2
No solution
(2 points)
Based on the student's work, the equation was solved
.
The equation solved correctly would show that it has
solution(s).
Based on the student's work, the equation was solved incorrectly.
The equation should show that it has infinitely many solutions.
Select the equation that has infinitely many solutions.(1 point)
Responses
4x+1=4(x+1)
4 x plus 1 is equal to 4 times open paren x plus 1 close paren
3x=2x+1
3 x is equal to 2 x plus 1
3−3x=−3(x−1)
3 minus 3 x is equal to negative 3 times open paren x minus 1 close paren
3x+5=3x−5
The equation that has infinitely many solutions is:
3x=2x+1
13 of 2013 of 20 Items
Question
Solve the equation and inequality for x(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.
ax+15=44
: Response area
ax−44<15
: Response area
To solve the equation ax + 15 = 44, we can subtract 15 from both sides:
ax + 15 - 15 = 44 - 15
This simplifies to:
ax = 29
To solve the inequality ax - 44 < 15, we can add 44 to both sides:
ax - 44 + 44 < 15 + 44
This simplifies to:
ax < 59
The speed limit sign on the expressway says that the speed limit is 55 mph. Write an equality that represents all speeds you can legally drive on the expressway.(1 point)
Responses
x≥55
x is greater than or equal to 55
x>55
x is greater than 55
x<55
x<55
x≤55
x is less than or equal to 55
The equality that represents all speeds you can legally drive on the expressway is: x ≤ 55
This means that the speed (x) must be less than or equal to 55 mph.
If you were to graph the inequality below on a number line:
35<7x
(2 points)
Would you use an open or a closed circle?
Would your arrow on the number line point to the left or to the right?
To graph the inequality 35 < 7x on a number line, we need to determine whether to use an open or a closed circle and the direction in which the arrow should point.
In this case, the inequality is strict (with a less than sign), so we will use an open circle.
The arrow on the number line would point to the right, indicating that the values of x are greater than 35.
A student solved the following equation using the following steps:
2(2x+2)=4(x+4)
4x+4=4x+4
4=4
Conclusion: Infinitely many solutions
(2 points)
Based on the student's work, the equation was solved
The equation solved correctly would show that it has
solution(s).
Based on the student's work, the equation was solved incorrectly.
The equation should show that it has a single solution, as the variables on both sides of the equation cancel out.
Solve the equation for y:
3x+5y=60
(2 points)
Responses
y=60−3x
y is equal to 60 minus 3 x
y=60+3x5
y is equal to 60 plus 3 x over 5
y=57x5
y is equal to 57 x over 5
y=−35x+12
To solve the equation 3x+5y=60 for y, we can isolate y on one side of the equation by subtracting 3x from both sides:
3x + 5y - 3x = 60 - 3x
This simplifies to:
5y = 60 - 3x
Finally, we divide both sides by 5 to get the solution for y:
y = (60 - 3x) / 5
Therefore, the correct response is: y = (60 - 3x) / 5
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 pencils in your box)
b) What if you wanted to have at least 20 pencils left in your box? How many pencils would you have needed originally?
c) Write an inequality and show all steps for solving for x.
a) Let's solve the equation to find the original number of pencils (x) in your box:
The number of pencils shared equally with your friend is x/2.
After sharing, you add 3 more pencils to your own box, making a total of (x/2) + 3 pencils.
The equation is: (x/2) + 3 = 15
To solve it, we can start by subtracting 3 from both sides:
(x/2) = 12
Next, multiply both sides by 2 to eliminate the fraction:
x = 24
So, the original number of pencils in your box was 24.
b) If you wanted to have at least 20 pencils left in your box, we can set up the following inequality:
(x/2) + 3 ≥ 20
To solve it, we can subtract 3 from both sides:
(x/2) ≥ 17
Next, multiply both sides by 2 to eliminate the fraction:
x ≥ 34
Therefore, you would have needed originally at least 34 pencils in your box.
c) The inequality for the number of pencils (x) in your box, considering you want to have at least 20 pencils left, is:
(x/2) + 3 ≥ 20
Again, this inequality simplifies to:
x/2 ≥ 17
And by multiplying both sides by 2, we get:
x ≥ 34