Question

The correct response is:

Multiplying both sides by 7 undoes the division of x by 7 in the original problem.

This is because the equation \( \frac{x}{7} - 47 = -6 \) contains the term \( \frac{x}{7} \), and multiplying the entire equation by 7 will eliminate the division by 7, making it easier to solve for \( x \).

Determine the first step in simplifying this expression.

13−2(1−15)÷4

(1 point)
Responses

13−2
13 minus 2

2×1
2 times 1

1−15
1 minus 15

15÷4

To simplify the expression \( 13 - 2(1 - 15) \div 4 \), the first step is to deal with the parentheses.

So the correct response is:

1−15
(1 minus 15)

You should simplify the expression inside the parentheses first before moving on to other operations.

Correctly select the order of the steps to solve this equation.

−5x+2=67

(1 point)
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:
Step 2:
add 67 to both sides of the equation
add 2 to both sides of the equation
add 5 to both sides of the equation
divide both sides of the equation by -5
multiply -5 on both sides of the equation
subtract 2 from both sides of the equation
subtract 5 from both sides of the equation

Solve for x.

−5x+2=67

(1 point)
Responses

x=−35
x is equal to negative 3 over 5

x=−695
x is equal to negative 69 over 5

x=−13
x is equal to negative 13

x=13

To solve the equation \(-5x + 2 = 67\), the correct order of steps is as follows:

Step 1: subtract 2 from both sides of the equation
Step 2: divide both sides of the equation by -5

This is how it works out:

1. Subtract 2 from both sides: \[ -5x + 2 - 2 = 67 - 2 \] \[ -5x = 65 \]

2. Divide both sides by -5: \[ x = \frac{65}{-5} \] \[ x = -13 \]

So the solution is:

x = -13
(x is equal to negative 13)

Correctly select the order of the steps to solve this equation.

r/5−6=−1


(1 point)
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:
Step 2:
Add 5 to both sides of the equation.
Multiply 5 on both sides of the equation.
Add 6 to both sides of the equation.
Subtract 6 from both sides of the equation.
Divide both sides of the equation by 5 .

Solve for r.

r5−6=−1


(1 point)
Responses

r = 5
r = 5

r = 25
r = 25

r = 35
r = 35

r = 10

To solve the equation \( \frac{r}{5} - 6 = -1 \), the correct order of steps is:

Step 1: Add 6 to both sides of the equation.
Step 2: Multiply both sides of the equation by 5.

Here’s how it works out:

1. Step 1: Add 6 to both sides: \[ \frac{r}{5} - 6 + 6 = -1 + 6 \] \[ \frac{r}{5} = 5 \]

2. Step 2: Multiply both sides by 5: \[ 5 \times \frac{r}{5} = 5 \times 5 \] \[ r = 25 \]

So, the solution is:

r = 25
(r = 25)

Correctly select the order of the steps to solve this equation.

−8−3x=10

(1 point)
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:
Step 2:

Add 8 to both sides of the equation.
Add 3 to both sides of the equation.
Add 10 to both sides of the equation.
Multiply both sides of the equation by 3 .
Divide both sides of the equation by 3 .
Divide both sides of the equation by -3 .
Subtract 8 from both sides of the equation.
Subtract 3 from both sides of the equation.

Solve for x.

−8−3x=10


(1 point)
Responses

x = -54
x = -54

x = -6
x = -6

x = 54
x = 54

x = 6

To solve the equation \( -8 - 3x = 10 \), the correct order of steps is:

Step 1: Add 8 to both sides of the equation.
Step 2: Divide both sides of the equation by -3.

Here’s how it works out:

1. Step 1: Add 8 to both sides: \[ -8 - 3x + 8 = 10 + 8 \] \[ -3x = 18 \]

2. Step 2: Divide both sides by -3: \[ \frac{-3x}{-3} = \frac{18}{-3} \] \[ x = -6 \]

So, the solution is:

x = -6
(x = -6)

Select the TWO expressions that are equivalent to the given expression.

(2x+2)−(3x+11)


(1 point)
Responses

5x+13
5 x plus 13

−x+9
negative x plus 9

−x−9
negative x minus 9

−x+13
negative x plus 13

5x+9
5 x plus 9

2x−3x+2−11
2 x minus 3 x plus 2 minus 11

2x−3x+2+11

To simplify the expression \( (2x + 2) - (3x + 11) \), we can first distribute the negative sign through the second parentheses:

\[ (2x + 2) - (3x + 11) = 2x + 2 - 3x - 11 \]

Now, combine the like terms:

\[ 2x - 3x + 2 - 11 = -x - 9 \]

Now we can determine which expressions are equivalent. The equivalent expressions are:

1. −x−9 (negative x minus 9)
2. 2x−3x+2−11 (2 x minus 3 x plus 2 minus 11)

Thus, the two equivalent expressions that you should select are:

• −x−9
• 2x−3x+2−11