Question

For this item, select the answers from the drop-down menus to complete the sentence. A student solves the equation 34=3(4x−2) , as shown. Given: 34=3(4x−2) Step 1 : 3(4x−2)=34 Step 2 : 12x−2=34 Step 3 : 12x=36 Step 4 : x=3

Answer 1

The student correctly solved the algebraic equation by using the distributive property, simplification, addition, and division, ultimately finding that the value of x is 3.

The question involves solving a single-variable linear equation. Starting with the given equation 34=3(4x-2), the student correctly applied the distributive property to reach

Step 2: 12x-2=34. To isolate the variable x, they added 2 to both sides, resulting in

Step 3: 12x=36. Finally, by dividing both sides by 12, the student correctly found the value of x in

Step 4: x=3.

It is important to note the methodological approach used to solve for x: distribute, simplify, and isolate the variable through addition or subtraction, and then divide or multiply to find the value. A proportion could be used in a similar fashion in different contexts, such as converting units or using the scale factor in geometry problems.

Answer 2

Answer: distributive property and properties of equality.

Explanation:

The student solved the equation by using the property of distributive property and properties of equality..

Given: 34=3(4x−2)

Step 1: 3(4x−2)=34 (Distributive Property)

Step 2: 12x−2=34

Step 3: 12x=36 (Addition Property of Equality)

Step 4: x=3 (Division Property of Equality)