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)
The left side of the equation can be simplified using the Distributive Property as follows:
2(x-5) = 2*x - 2*5 = 2x - 10
The right side of the equation can be simplified by combining like terms as follows:
9 - 3x + 6 + 8 + 3x + 7 = (9 + 6 + 8 + 7) + (-3x + 3x) = 30
Therefore, we have:
2x - 10 = 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
To solve the equation 3(x-5) + 2x = 0, we need to simplify both sides of the equation and solve for the variable x.
First, let's simplify the left side of the equation:
3(x-5) + 2x = 0
3x - 15 + 2x = 0
Combining like terms:
3x + 2x - 15 = 0
5x - 15 = 0
Next, let's isolate the variable x by moving the constant term to the other side of the equation:
5x - 15 + 15 = 0 + 15
5x = 15
Finally, let's solve for x by dividing both sides of the equation by 5:
(5x)/5 = 15/5
x = 3
Therefore, the values to fill in the blanks are:
3x + 2x = 0
5x = 15
x = 3
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=
To fill in the blanks for the given equation 3(x-5) + 2x = 0, we have:
3(x-5) = 3x - 15
2x = 2x
Therefore, the correct values to fill in the blanks are:
3x - 15 + 2x = 0
And the equation can be rewritten as:
5x - 15 = 0
are you sure this is correctf
Apologies for the confusion. You're right, my previous response was incorrect.
To solve the equation 3(x-5) + 2x = 0, let's simplify both sides and solve for x:
First, distribute the 3 to the terms inside the parentheses:
3x - 15 + 2x = 0
Combine like terms:
5x - 15 = 0
Now, let's isolate the variable x by moving the constant term to the other side of the equation:
Add 15 to both sides:
5x = 15
Finally, solve for x by dividing both sides of the equation by 5:
x = 15/5
x = 3
Therefore, the correct values to fill in the blanks are:
3x + 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 the subtraction property of equality to isolate 2x, subtracting 15 from both sides to get 2x = -18
Step 4: Use the division property of equality to solve for x, dividing 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.
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 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 solution to the equation.
The correct 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
Add x to both sides of the equation.
Add x 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.
Subtract x from both sides of the equation.
Subtract 27 from both sides of the equation.
Subtract 27 from both sides of the equation.
Subtract 24 from both sides of the equation.
Subtract 24 from both sides of the equation.
Add 24 to both sides of the equation.
Add 24 to both sides of the equation.
The next best step to finish solving the equation 3 - 15x + 24 + 16x = 4x - 24 - 4x would be to simplify the equation further by combining like terms.
Combining like terms, we have:
(-15x + 16x) + (3 + 24) = (4x - 4x) - 24
This simplifies to:
x + 27 = -24
To finish solving, the next step would be to subtract 27 from both sides of the equation. Therefore, the correct response is: Subtract 27 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 correct statement would be that the equation solved incorrectly would show that it has no solution.
Select the equation that has infinitely many solutions.(1 point)
Responses
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)
4 x plus 1 is equal to 4 times open paren x plus 1 close paren
3x=2x+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
:
To solve the equation ax + 15 = 44, we need to isolate the variable x.
Subtract 15 from both sides of the equation:
ax = 44 - 15
Simplify:
ax = 29
Divide both sides of the equation by a to solve for x:
x = 29/a
Therefore, the solution for the equation is x = 29/a.
To solve the inequality ax - 44 < 15, we need to isolate the variable x.
Add 44 to both sides of the inequality:
ax < 15 + 44
Simplify:
ax < 59
Divide both sides of the inequality by a:
x < 59/a
Therefore, the solution for the inequality is x < 59/a.
Which inequality represents the graph below:
(1 point)
Responses
−3x+7<10
−3x+7<10
−3x−7≥−10
negative 3 x minus 7 is greater than or equal to negative 10
3x+7>10
3 x plus 7 is greater than 10
3x−7<−10
The correct inequality that represents the graph below is:
3x - 7 < -10.