Question

Justify the Steps in solving the equation 3(2x-4) = 18:

step 1: 3(2x-4)=18 (given)
Step 2: 6x-12=18
Step 3: 6x=30
Step 4: x=5
a) Addition
b) Subtraction
c) Multiplication
d) Division

Answer 1

The steps to solve the equation 3(2x-4) = 18 include distribution (multiplication), adding 12 to both sides (addition), and dividing by 6 (division) to isolate and solve for the unknown variable x.

Step-by-step explanation:

Justifying the steps in solving the equation 3(2x-4) = 18 involves explaining the mathematical operations performed at each step:

1. Step 1: 3(2x-4) = 18 (given).
2. Step 2: 6x - 12 = 18. This is achieved by applying the distribution property to multiply the 3 into both terms inside the parentheses (multiplication).
3. Step 3: 6x = 30. We obtained this by adding 12 to both sides of the equation to isolate the term with the variable (addition).
4. Step 4: x = 5. This final step involves dividing both sides of the equation by 6 to solve for x, therefore isolating the unknown (division).

In brief, we identified the unknown (x), applied algebraic rearrangement techniques, such as multiplication and addition, to isolate the term with the variable, and finally used division to solve for the unknown.