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Which equation below represents the hanger?

a (circle)
3 (rectangle)
7 (square)

(1 point)
Responses

3a=7
3 A is equal to 7

a+3=7
A plus 3 is equal to 7

a3=7
A over 3 is equal to 7

a−3=7

11 answers

To determine which equation represents the hanger, we need to understand how equations typically relate to the elements being described. Assuming "a" represents the circle, "3" represents the rectangle, and "7" represents the square, we must examine each option:

  1. 3a = 7: This implies three times the circle (3a) equals the square (7). This equation does not suggest a direct relationship where the hanger is isolated or stood.

  2. a + 3 = 7: This implies the circle, plus the rectangle, equals the square. This is a straightforward addition where the elements combine to match the square.

  3. a3 = 7: This seems to imply that "a" is divided by 3, but it is not a standard notation for division and could be confusing.

  4. a - 3 = 7: This implies that the circle minus the rectangle equals the square. This means if you take the rectangle away from the circle, you are left with the square, which might not be a clear representation of a hanger.

Given these interpretations, the equation that likely represents a simple relationship, implying addition of the rectangle to reach the square, would be:

a + 3 = 7

So the answer is: a + 3 = 7; A plus 3 is equal to 7.

Determine the first step in solving this equation.

5n−18=−33

(1 point)
Responses

Multiply both sides of the equation by 5.
Multiply both sides of the equation by 5.

Add 5 to both sides of the equation.
Add 5 to both sides of the equation.

Subtract 18 from both sides of the equation.
Subtract 18 from both sides of the equation.

Add -33 to both sides of the equation.
Add -33 to both sides of the equation.

Add 18 to both sides of the equation.

To solve the equation \( 5n - 18 = -33 \), you want to isolate the term with \( n \) on one side of the equation.

The first step should be to eliminate the constant term on the left side, which is \(-18\). The appropriate action is to add \( 18 \) to both sides of the equation.

So, the correct response is:

Add 18 to both sides of the equation.

Determine the first step to solve this equation.

120−8d=7


(1 point)
Responses

Add 120 to both sides of the equation.
Add 120 to both sides of the equation.

Subtract 120 from both sides of the equation.
Subtract 120 from both sides of the equation.

Add 8 to both sides of the equation.
Add 8 to both sides of the equation.

Subtract 8 from both sides of the equation.
Subtract 8 from both sides of the equation.

Multiply -8 on both sides of the equation.

To solve the equation \(120 - 8d = 7\), the first step is to isolate the term involving \(d\). It is appropriate to eliminate the constant term (in this case, \(120\)) from the left side of the equation.

The correct action is to subtract 120 from both sides of the equation. This will help you isolate the term with \(d\).

So, the correct response is:

Subtract 120 from both sides of the equation.

Sort the following equations into one-step and two-step equations.(1 point)
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One-Step Equation Two-Step Equation

1/3x + 1 = -2
2x = 16
x/2 = 3
2x - 3 = 5
x - 3 = 5

Here’s how to categorize the given equations into one-step and two-step equations:

One-Step Equations:

  1. \(2x = 16\)
  2. \(x/2 = 3\)
  3. \(x - 3 = 5\)

Two-Step Equations:

  1. \(1/3x + 1 = -2\)
  2. \(2x - 3 = 5\)

So, the sorted list is as follows:

One-Step Equation:

  • \(2x = 16\)
  • \(x/2 = 3\)
  • \(x - 3 = 5\)

Two-Step Equation:

  • \(1/3x + 1 = -2\)
  • \(2x - 3 = 5\)
Match the order of steps to solve the equation.

10x−18=−2


(1 point)
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Step 1

Step 2

Step 3

subtract 18 from both sides of the equation
add 18 to both sides of the equation
multiply both sides of the equation by 10
divide both sides of the equation by 10
x = 8/5
x = -2
x = -8/5

To solve the equation \(10x - 18 = -2\), follow these steps in the correct order:

Step 1

Add 18 to both sides of the equation.
This will help isolate the term with \(x\).

New equation:
\(10x = 16\)

Step 2

Divide both sides of the equation by 10.
This will solve for \(x\).

New equation:
\(x = \frac{16}{10}\) or \(x = \frac{8}{5}\)

Step 3

x = \frac{8}{5} (This is the simplified solution.)

So the correct matching is:

  • Step 1: add 18 to both sides of the equation
  • Step 2: divide both sides of the equation by 10
  • Step 3: x = 8/5
The equation −3x−9=−21
is solved as follows. Enter the correct numbers to complete the solution.(1 point)
−3x−9=−21

−3x=

Add 9 to both sides of the equation.

x=
Divide both sides of the equation by -3. If the answer is an improper fraction, enter the improper fraction.

To solve the equation \(-3x - 9 = -21\), we follow these steps:

  1. Start with the original equation: \[ -3x - 9 = -21 \]

  2. Add 9 to both sides: \[ -3x = -21 + 9 \] \[ -3x = -12 \]

  3. Now, divide both sides by -3: \[ x = \frac{-12}{-3} \] \[ x = 4 \]

So, the completed solution is:

  • \(-3x = -12\)
  • \(x = 4\)

Therefore, the answers to fill in the blanks are:

  • −3x = -12
  • x = 4