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=−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
2x+12=27
2 x plus 12 is equal to 27
8. 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+14=−24+20x
35 x plus 14 is equal to negative 24 plus 20 x
35x+2=24−20x
35 x plus 2 is equal to 24 minus 20 x
5x+14=6+20x
5 x plus 14 is equal to 6 plus 20 x
35x+14=−24−20x
35 x plus 14 is equal to negative 24 minus 20 x
35x+2=−24−5x
35 x plus 14 is equal to negative 24 plus 20 x
9. For the equation 2(x−5)=9−3x+6+8+3x+7
, the left side of the equation can be simplified 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 left side of the equation: Response area
Simplify the right side of the equation: Response area
Simplify the left side of the equation: 2 * (x - 5)
Simplify the right side of the equation: 9 - 3x + 6 + 8 + 3x + 7
10. Jill solves the equation 3(x−5)+2x=0
. Fill in the blanks for each step with the correct values:(3 points)
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3x+
Response area+2x=0
5x=
Response area
x=
Response area
3x + 5 + 2x = 0
5x + 5 = 0
x = -1
no
Apologies for the incorrect response. Let's solve the equation again:
3(x - 5) + 2x = 0
First, we distribute the 3:
3x - 15 + 2x = 0
Now, we combine like terms:
5x - 15 = 0
Next, we isolate the variable by adding 15 to both sides:
5x = 15
Finally, we solve for x by dividing both sides by 5:
x = 3
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
Divide both sides of the equation by 15.
Divide both sides of the equation by 15.
Add x to both sides of the equation.
Add x to 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.
Subtract x from both sides of the equation.
Subtract x from both sides of the equation.
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
incorrectly
The equation solved correctly would show that it has
solution(s).
Based on the given work, it appears that the equation was solved incorrectly. The correct solution should show that the equation has solution(s).
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
correctly
The equation solved correctly would show that it has
no
solution(s).
Based on the given work, it appears that the equation was solved correctly. The equation simplifies to 4=4, which means that there are infinitely many solutions.
9. For the equation 2(x−5)=9−3x+6+8+3x+7
, the left side of the equation can be simplified 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 left side of the equation: Response area
Simplify the right side of the equation: Response area
Simplify the left side of the equation: 2 * (x - 5)
Simplify the right side of the equation: 9 - 3x + 6 + 8 + 3x + 7
i said no
I apologize for the confusion. Let's simplify the equation again:
Left side of the equation: 2(x - 5)
Right side of the equation: 9 - 3x + 6 + 8 + 3x + 7
14. If you were to graph the inequality 35<7x
on a number line:(2 points)
Would you use an open or 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 if we should use an open or closed circle and if the arrow should point to the left or to the right.
Since this is a "less than" inequality, we use an open circle to represent values that are not equal to 35.
The arrow on the number line would point to the right to indicate that the values of x greater than 5 are the solutions to the inequality.
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.
a. Let's solve for x step by step:
1. You initially had x colored pencils in your pencil box.
2. You shared them equally between you and your friend, so each of you received x/2 colored pencils.
3. After sharing, you added 3 more colored pencils to your own box, which gave you a total of (x/2) + 3 colored pencils.
4. The total number of colored pencils you have is 15, so we can set up the equation:
(x/2) + 3 = 15
5. To solve for x, let's first subtract 3 from both sides of the equation:
(x/2) = 12
6. To get rid of the fraction, we can multiply both sides of the equation by 2:
2 * (x/2) = 2 * 12
x = 24
Therefore, the original number of colored pencils in your box was 24.
b. If you want to have at least 20 colored pencils left in your box, we can set up the equation:
x - (x/2) - 3 ≥ 20
To solve for x, let's simplify the equation:
2x - x - 6 ≥ 40
x - 6 ≥ 40
x ≥ 46
Therefore, you would need to have originally at least 46 colored pencils in your box.
c. The inequality is: x - (x/2) - 3 ≥ 20
18. Solve the following:(2 points)
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ax+15=44
ax−44<15
To solve the equation ax + 15 = 44:
1. Subtract 15 from both sides of the equation:
ax = 44 - 15
To solve the inequality ax - 44 < 15:
1. Add 44 to both sides of the inequality:
ax < 15 + 44
no
I apologize for the incorrect response. Let's solve each equation separately:
To solve the equation ax + 15 = 44:
1. Subtract 15 from both sides of the equation:
ax = 44 - 15
ax = 29
To solve the inequality ax - 44 < 15:
1. Add 44 to both sides of the inequality:
ax < 15 + 44
ax < 59
I apologize for the confusion earlier.
17. Solve the equation filling in the steps: 2(x−3)+21=−3
(6 points)
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Distribute to get
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
To solve the equation 2(x - 3) + 21 = -3, let's go through each step:
1. Distribute to get 2x - 6 + 21 = -3
2. Combine like terms to get 2x + 15 = -3
3. Use the subtraction property of equality to subtract 15 from both sides: 2x = -3 - 15
4. Simplify: 2x = -18
5. Divide both sides by 2 to solve for x: x = -9
So, the resulting answer is x = -9.