Five less than three-fourths of x is seven. If x equals 16, what is the last property of equality you would use to justify the solution to this problem?(1 point)

Question

Responses

Identity Property of Multiplication
Identity Property of Multiplication

Subtraction Property of Equality
Subtraction Property of Equality

Addition Property of Equality
Addition Property of Equality

Division Property of Equality

Answer 1

To solve the equation "Five less than three-fourths of x is seven," we can set up the equation:

\[ \frac{3}{4}x - 5 = 7 \]

To isolate \(x\), we can use the following steps:

1. Add 5 to both sides to eliminate the subtraction: \[ \frac{3}{4}x - 5 + 5 = 7 + 5 \] This simplifies to: \[ \frac{3}{4}x = 12 \] (This step utilizes the Addition Property of Equality.)

2. Multiply both sides by \(\frac{4}{3}\) to solve for \(x\): \[ \left(\frac{4}{3}\right)\frac{3}{4}x = \left(\frac{4}{3}\right)(12) \] This simplifies to: \[ x = 16 \] (This step utilizes the Multiplication Property of Equality.)

The final step that includes the transition from the simplified equation \(\frac{3}{4}x = 12\) to solving for \(x\) involves multiplying both sides by a fraction. The property used at this stage is primarily associated with multiplication but, since we are looking for the last property used in the entire process, it was the Addition Property of Equality used first to isolate the \(x\) term after addressing the constant.

In conclusion, the last property of equality would be:

Addition Property of Equality.

Answer 2

Manipulate the equation y=7x−12 so that it is written in terms of x. Which equation is equivalent to y=7x−12?(1 point)
Responses

x=(y12)−7
x equals left parenthesis Start Fraction y over 12 End Fraction right parenthesis minus 7

x=(y+12)7
x equals Start Fraction left parenthesis y plus 12 right parenthesis over 7 End Fraction

x=(y7)+12
x equals left parenthesis Start Fraction y over 7 End Fraction right parenthesis plus 12

x=(y−12)7

Answer 3

To manipulate the equation \( y = 7x - 12 \) to express it in terms of \( x \), we need to isolate \( x \). Here are the steps:

1. Add 12 to both sides to get rid of the -12 on the right: \[ y + 12 = 7x \]

2. Divide both sides by 7 to solve for \( x \): \[ x = \frac{y + 12}{7} \]

Now, let's compare this to the provided options:

1. \( x = \frac{y}{12} - 7 \)
2. \( x = \frac{y + 12}{7} \)
3. \( x = \frac{y}{7} + 12 \)
4. \( x = \frac{y - 12}{7} \)

The correct option that matches our derived equation is:

x = (y + 12) / 7 (Option 2).

Answer 4

Which equation is equivalent to w=x+y−z?(1 point)
Responses

z=w−x−y
z equals w minus x minus y

z=x+y+w
z equals x plus y plus w

z=x+y−w
z equals x plus y minus w

z=(x+y)w

Answer 5

To manipulate the equation \( w = x + y - z \) so that it is expressed in terms of \( z \), we can follow these steps:

1. Start with the equation: \[ w = x + y - z \]

2. Rearranging this to isolate \( z \) involves adding \( z \) to both sides and subtracting \( w \) from both sides: \[ z = x + y - w \]

Now, let’s compare this to the provided options:

1. \( z = w - x - y \)
2. \( z = x + y + w \)
3. \( z = x + y - w \)
4. \( z = (x + y) w \)

The equation that matches our derived equation is:

z = x + y - w (Option 3).