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)
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Step 1: Response area to get Response area
Step 2: Response area to get Response area
Step 3: Response area to get
Step 1: Combine like terms.
The simplified equation becomes 7n + 9 = 2.
Step 2: Subtract 9 from both sides of the equation.
The simplified equation becomes 7n = -7.
Step 3: Divide both sides of the equation by 7.
The simplified equation becomes n = -1.
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)
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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:
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 equation for the area equal to 38: (3h - 4) × h / 2 = 38
Match the equation with its solution.(3 points)
3i+2i−4=18i
3(2i−7)=6i−21
2i+3=2i−5
the options are no solution
infinite solutions
i = 5
i = 8
i = 4/13
i = 1/3
3i+2i−4=18i - no solution
3(2i−7)=6i−21 - i = 8
2i+3=2i−5 - no solution
Match the equation with its solution. each solution can only be used ONCE
3i+2i−4=18i
3(2i−7)=6i−21
2i+3=2i−5
the options are no solution
infinite solutions
i = 5
i = 8
i = 4/13
i = 1/3
3i+2i−4=18i - no solution
3(2i−7)=6i−21 - infinite solutions
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
2(x−5)+2x=10
2 times open paren x minus 5 close paren plus 2 x is equal to 10
2x+12=−3x−27
2 x plus 12 is equal to negative 3 x minus 27
4x−17+2x=9
4 x minus 17 plus 2 x is equal to 9
2x+12=27
2x+12=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?
35x+2=24−20x
35 x plus 2 is equal to 24 minus 20 x
35x+2=−24−5x
35 x plus 2 is equal to negative 24 minus 5 x
35x+10=−24+20x
35 x plus 10 is equal to negative 24 plus 20 x
5x+14=6+20x
5 x plus 14 is equal to 6 plus 20 x
35x+14=−24+20x
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.
Simplify the left side of the equation:
Simplify the right side of the equation:
Simplify the left side of the equation: 2x - 10
Simplify the right side of the equation: 23
23 is not an option
I apologize for the confusion. Let me simplify the right side of the equation correctly:
Simplify the left side of the equation: 2(x - 5) = 2x - 10
Simplify the right side of the equation: 9 - 3x + 6 + 8 + 3x + 7 = 33
33 is also not an option
Apologies for the mistake again. Let me simplify the right side of the equation correctly:
Simplify the left side of the equation: 2(x - 5) = 2x - 10
Simplify the right side of the equation: 9 - 3x + 6 + 8 + 3x + 7 = 33x + 30
whats the answer
The simplified equation would be:
2(x - 5) = 33x + 30
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
Jill solves the equation 3(x−5)+2x=0
. Fill in the blanks with the correct values:
3x+ +2x=0
5x=
x=
3x + (2x) = 0
5x = 15
x = 3
Jill solves the equation 3(x−5)+2x=0
. Fill in the blanks with the correct values:
3x+ blank +2x=0
3x + 2x = 0
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 2x: 2x = -3 - 15 = -18.
Step 4: Use division to solve for x: x = -18 / 2 = -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 is no solution to the equation.
There is no solution 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.
The only solution to the equation is -6.
The only solution to the equation is -6.
There are infinitely many solutions to the equation.
There are infinitely many solutions to the equation.
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
Divide both sides of the equation by 15.
Divide both sides of the equation by 15.
Add 24 to both sides of the equation.
Add 24 to both sides of the equation.
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 x to both sides of the equation.
Add x to both sides of the equation.
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 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
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
3x=2x+1
3 x is equal to 2 x plus 1
3x=2x+1
Solve the equation and inequality for x(
ax+15=44
ax−44<15
To solve the equation ax + 15 = 44:
Step 1: Subtract 15 from both sides:
ax + 15 - 15 = 44 - 15
ax = 29
Step 2: Divide both sides by "a" to solve for x:
x = 29/a
To solve the inequality ax - 44 < 15:
Step 1: Add 44 to both sides:
ax - 44 + 44 < 15 + 44
ax < 59
Step 2: Divide both sides by "a" if a is positive, or divide both sides by "a" and flip the inequality sign if a is negative:
If a > 0: x < 59/a
If a < 0: 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 greater than 55
x≥55
x is greater than or equal to 55
x<55
x<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?
You would use an open circle to represent the inequality.
The arrow on the number line would point to the right.
Match the equation to the correct graphed solution.(2 points)
I apologize, but I am unable to observe or analyze visual content.
equation 1 is an open circle on the number 12 pointing to the left
equation 2 is an open circle at -2 pointing left
I apologize, but without the specific equations or a visual representation of the graphs, I am unable to match the equations to their corresponding graphed solutions.
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 a single solution.
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
y is equal to 57 x over 5
To solve the equation 3x + 5y = 60 for y:
Step 1: Subtract 3x from both sides of the equation:
3x + 5y - 3x = 60 - 3x
5y = 60 - 3x
Step 2: Divide both sides by 5 to isolate y:
y = (60 - 3x) / 5
Therefore, the correct 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.
a) Let's use the equation to represent the situation:
(x/2) + 3 + x = 15
Step 1: Divide x by 2 to represent sharing the pencils equally between you and your friend:
x/2 + 3 + x = 15
Step 2: Combine like terms:
(3/2)x + 3 = 15
Step 3: Subtract 3 from both sides of the equation:
(3/2)x = 15 - 3
(3/2)x = 12
Step 4: Multiply both sides by 2/3 to solve for x:
x = (12 * 2) / 3
x = 8
Therefore, the original number of pencils you had in your box was 8.
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
Step 1: Subtract 3 from both sides of the inequality:
x/2 ≥ 17
Step 2: Multiply both sides by 2 to solve for x:
x ≥ 34
Therefore, you would have originally needed at least 34 pencils in your box.
c) The inequality we derived in part b) is:
x/2 + 3 ≥ 20
This represents that the number of pencils you originally had divided by 2, plus 3, is greater than or equal to 20.