Put the steps in order to solve the equation: 3n+9+4n=2
. Put the reasoning in the first blank and the simplified equation in the second blank.(6 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.
1. Combine like terms on the left side of the equation: 3n + 4n = 7n
2. Simplify the equation: 7n + 9 = 2
3. Subtract 9 from both sides of the equation to isolate the variable: 7n = -7
4. Divide both sides of the equation by 7 to solve for n: n = -1
Put the steps in order to solve the equation: 3n+9+4n=2
. Put the reasoning in the first blank and the simplified equation in the second blank.(6 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.
Step 1: Response area to get Response area
Step 2: Response area to get Response area
Step 3: Response area to get Response area
Step 1: Combine like terms on the left side of the equation: 3n + 4n = 7n
Step 2: Simplify the equation: 7n + 9 = 2
Step 3: Subtract 9 from both sides of the equation to isolate the variable: 7n = -7
WORD BANK: Divide both sides by 7, 7n = 11, n = -1, Combine like terms, Use subtraction as the inverse operation, multiply both sides by 7, 7n = -7, 7n + 9 = 2, Use addition as the inverse operation, n = 11/7, n = -49
Step 1: Combine like terms on the left side of the equation: 3n + 4n = 7n
Step 2: Simplify the equation: 7n + 9 = 2
Step 3: Use subtraction as the inverse operation - Subtract 9 from both sides of the equation to isolate the variable: 7n = -7
WORD BANK: Divide both sides by 7, 7n = 11, n = -1, Combine like terms, Use subtraction as the inverse operation, multiply both sides by 7, 7n = -7, 7n + 9 = 2, Use addition as the inverse operation, n = 11/7, n = -49
Put the steps in order to solve the equation: 3n+9+4n=2
. Put the reasoning in the first blank and the simplified equation in the second blank.(6 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.
Step 1: to get Response area
Step 2: Response area to get Response area
Step 3: Response area to get Response area
Step 1: Combine like terms on the left side of the equation: 3n + 4n = 7n
Step 2: Simplify the equation: 7n + 9 = 2
Step 3: Use subtraction as the inverse operation - Subtract 9 from both sides of the equation to isolate the variable: 7n = -7
Put the steps in order to solve the equation: 3n+9+4n=2
. Put the reasoning in the first blank and the simplified equation in the second blank.(6 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.
Step 1: ____ to get ____
Step 2: ____ to get ____
Step 3: ____ to get ____
WORD BANK: Divide both sides by 7, 7n = 11, n = -1, Combine like terms, Use subtraction as the inverse operation, multiply both sides by 7, 7n = -7, 7n + 9 = 2, Use addition as the inverse operation, n = 11/7, n = -49
Step 1: Combine like terms on the left side of the equation: 3n + 4n = 7n
Step 2: Simplify the equation: 7n + 9 = 2
Step 3: Use subtraction as the inverse operation - Subtract 9 from both sides of the equation to isolate the variable: 7n = -7
The base of a triangle is 4 less than three times the height. The area of the triangle is 38 square cm. A=b × h2
(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.
An expression for the base of the triangle:. Response area
Equation for the area of the triangle: Response area
The first step in solving for h: Response area
The option "Multiply both sides by 2" (6 of 8) has been selected. Press tab to choose a response area, and spacebar to insert it. Press escape to cancel.
An expression for the base of the triangle: 3h - 4
Equation for the area of the triangle: A = (3h - 4) * h / 2
The first step in solving for h: Set the area equation equal to 38: (3h - 4) * h / 2 = 38
The option "Multiply both sides by 2" (6 of 8) has been selected. Press tab to choose a response area, and spacebar to insert it. Press escape to cancel.
Match the equation with its solution.(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.
3i+2i−4=18i
3(2i−7)=6i−21
2i+3=2i−5
3i+2i−4=18i: No Solution
3(2i−7)=6i−21: i = -1
2i+3=2i−5: No Solution
Which equation has the SAME FIRST STEP to solve as this equation: 2x+12−3x=27?
(1 point)
Responses
2x+12=−3x−27
2 x plus 12 is equal to negative 3 x minus 27
2(x−5)+2x=10
2 times open paren x minus 5 close paren plus 2 x is equal to 10
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 can be solved using the equation: 2x+12=−3x−27.
Using the Distributive Property as a good first step to solving the equation 7(5x+2)=−4(6−5x)
, you could simplify this equation to get which of these choices? (1 point)
Responses
35x+2=−24−5x
35 x plus 2 is equal to negative 24 minus 5 x
35x+2=24−20x
35 x plus 2 is equal to 24 minus 20 x
35x+10=−24+20x
35 x plus 10 is equal to negative 24 plus 20 x
35x+14=−24+20x
35 x plus 14 is equal to negative 24 plus 20 x
5x+14=6+20x
Using the Distributive Property as a good first step to solving the equation 7(5x+2)=−4(6−5x), you could simplify this equation to get: 35x+14=−24+20x.
For the equation 2(x−5)=9−3x+6+8+3x+7
, the left side of the equation can be simplified by using the Distributive Property, and the right side of the equation can be simplified by combining like terms. (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.
Simplify the right side of the equation:
Simplify the left side of the equation:
Simplify the right side of the equation: 9 - 3x + 6 + 8 + 3x + 7 = 22
Simplify the left side of the equation using the Distributive Property: 2(x - 5) = 2x - 10
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+ Response area +2x=0
5x= Response area
x= Response area
Solution:
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 as the inverse operation - Subtract 15 from both sides of the equation to isolate the variable: 2x = -18
Step 4: Divide both sides of the equation by 2 to solve for x: 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
There are infinitely many solutions to the equation.
There are infinitely many solutions to the equation.
The only solution to the equation is 1.
The only solution to the equation is 1.
The only solution to the equation is -6.
The only solution to the equation is -6.
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 true statement is: 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
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 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.
Subtract x from both sides of the equation.
The next best step to finish solving the equation 3−15x+24+16x=4x−24−4x would be to 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 solution(s).
select the equation that has infinitely many solutions.(1 point)
Responses
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
3 x plus 5 is equal to 3 x minus 5
4x+1=4(x+1)
The equation that has infinitely many solutions is: 3x=2x+1.
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
The option "x is equal to 59 A" (2 of 7) has been selected. Press tab to choose a response area, and spacebar to insert it. Press escape to cancel.
ax+15=44: Subtract 15 from both sides of the equation: ax = 29
ax−44<15: Add 44 to both sides of the inequality: ax < 59
Which inequality represents the graph below:
<--------------------------------.------------------------------
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
(1 point)
Responses
3x−7<−10
3x−7<−10
−3x+7<10
−3x+7<10
3x+7>10
3 x plus 7 is greater than 10
−3x−7≥−10
negative 3 x minus 7 is greater than or equal to negative 10
The inequality that represents the graph below is: −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 greater than 55
x≤55
x is less than or equal to 55
x<55
x<55
x≥55
The equality that represents all speeds you can legally drive on the expressway is: 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. Use an open circle to represent the value of x at 35. This is because the inequality is strict (<), indicating that 35 is not included in the solution set.
2. The arrow on the number line would point to the right. This is because the inequality states that x is greater than 35, so the solution set includes all values to the right of 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 solved correctly would show that it has no solution(s).
Solve the equation for y:
3x+5y=60
(2 points)
Responses
y=60+3x5
y is equal to 60 plus 3 x over 5
y=−35x+12
y is equal to negative 3 fifths x plus 12
y=60−3x
y is equal to 60 minus 3 x
y=57x5
To solve the equation 3x + 5y = 60 for y, we need to isolate the variable y.
y = (60 - 3x)
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)
Solve the equation filling in the steps: 2(x−3)+21=−3(6 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.
Distribute to get Response area
Combine like terms to get Response area
Use the (choose a property) Response area to get (resulting equation) Response area
Use the (choose a property) Response area to get (resulting answer) Response area