Jill solves the equation 3(x−5)+2x=0
. Fill in the blanks with the correct values:(3 points)
3x+ _______+2x=0
5x=________
x= ________
3x-15+2x=0
5x=15
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: Use subtraction to isolate the variable. Subtract 15 from both sides: 2x = -18
Step 4: Use division to solve for x. Divide both sides by 2: 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 1.
The only solution to the equation is 1.
There are infinitely many solutions to the equation.
There are infinitely many solutions to the equation.
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 is no solution to the equation.
There is no solution to the equation.
The only solution to the equation is -6.
The only solution to the equation is -6.
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
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.
Subtract 24 from both sides of the equation.
Subtract 24 from both sides of the equation.
Add x to both sides of the equation.
Add x to both sides of the equation.
Subtract x from both sides of the equation.
Subtract x from both sides of the equation.
Subtract 27 from both sides of the equation.
Subtract 24 from 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 solved correctly would 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+5=3x−5
3 x plus 5 is equal to 3 x minus 5
3−3x=−3(x−1)
3 minus 3 x is equal to negative 3 times open paren x minus 1 close paren
3x=2x+1
3x+5=3x−5
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
ax + 15 = 44
To solve for x, we can subtract 15 from both sides:
ax = 44 - 15
ax = 29
x = 29/a
-
ax - 44 < 15
To solve for x, we can add 44 to both sides:
ax < 15 + 44
ax < 59
x < 59/a
Which inequality represents the graph below:
(1 point)
Responses
3x+7>10
3 x plus 7 is greater than 10
3x−7<−10
3x−7<−10
−3x+7<10
−3x+7<10
−3x−7≥−10
−3x+7<10
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 less than or equal to 55
x<55
x<55
x≥55
x is greater than or equal to 55
x>55
x ≤ 55
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:
1. Since the inequality is just less than, use an open circle.
2. The arrow on the number line would point to the right because the values of x greater than what is represented by the open circle satisfy the inequality.
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 solved correctly would show that it has infinitely many solutions.
Solve the equation for y:
3x+5y=60
(2 points)
Responses
y=57x5
y is equal to 57 x over 5
y=60+3x5
y is equal to 60 plus 3 x over 5
y=60−3x
y is equal to 60 minus 3 x
y=−35x+12
To solve the equation 3x + 5y = 60 for y:
Subtract 3x from both sides:
5y = 60 - 3x
Divide both sides by 5:
y = (60 - 3x)/5
Therefore, the solution 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.
(5 points)
a) Let's write an equation to represent the situation:
(x/2) + 3 = 15
To solve for x, 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) To have at least 20 pencils left in your box, we need:
(x/2) + 3 ≥ 20
Subtracting 3 from both sides:
(x/2) ≥ 17
Multiplying both sides by 2:
x ≥ 34
Therefore, you would have needed at least 34 pencils originally to have at least 20 remaining.
c) The inequality representing the situation is:
(x/2) + 3 ≥ 20
Subtracting 3 from both sides:
(x/2) ≥ 17
Multiplying both sides by 2:
x ≥ 34