Question

Kadir solves the equation (3x+5)/2-3=4. The steps he used to solve the equation are shown in the table below. Select an answer choice from each drop box to justify each step.

Answer 1

1. Addition Property of Equality

2. Multiplication Property of Equality

3. Subtraction Property of Equality

4. Division Property of Equality

Explanation:

The property of equality means that whatever operation you perform on one side of an equation, you must perform the same operation on the other side to maintain the equality and keep the equation balanced.

The given equation is:

`(3x+5)/(2)-3=4`

Step 1

To begin, Kadir uses the Addition Property of Equality, by adding 3 to both sides of the equation:

`(3x+5)/(2)-3+3=4+3`

`(3x+5)/(2)=7`

Step 2

Now, Kadir uses the Multiplication Property of Equality to eliminate the fraction on the left side of the equation by multiplying both sides of the equation by 2:

`(3x+5)/(2)* 2=7* 2`

`3x+5=14`

Step 3

Next, Kadir uses the Subtraction Property of Equality to isolate 3x by subtracting 5 from both sides of the equation:

`3x+5-5=14-5`

`3x=9`

Step 4

Finally, to isolate x, Kadir uses Division Property of Equality by dividing both sides of the equation by 3:

`(3x)/(3)=(9)/(3)`

`x = 3`