We are given the linear equation 3 times open parenthesis x minus 2 close parenthesis equals 18. Our goal is to find the value of x that makes this equation true.
First, we apply the distributive property. This means we multiply 3 by both terms inside the parentheses. So 3 times x gives us 3x, and 3 times negative 2 gives us negative 6. The equation becomes 3x minus 6 equals 18.
Now we want to isolate the term with x. To do this, we add 6 to both sides of the equation. On the left side, negative 6 plus 6 cancels out, leaving us with just 3x. On the right side, 18 plus 6 equals 24. So our equation becomes 3x equals 24.
To solve for x, we divide both sides of the equation by 3. On the left side, 3x divided by 3 simplifies to just x. On the right side, 24 divided by 3 equals 8. Therefore, x equals 8.
Let's verify our solution by substituting x equals 8 back into the original equation. We replace x with 8 in 3 times open parenthesis x minus 2 close parenthesis equals 18. This gives us 3 times open parenthesis 8 minus 2 close parenthesis equals 18. Simplifying inside the parentheses, 8 minus 2 equals 6. Then 3 times 6 equals 18. Since both sides equal 18, our solution x equals 8 is correct.
Let's summarize our solution process. First, we started with the original equation: 3 times open parenthesis x minus 2 close parenthesis equals 18. Next, we applied the distributive property to get 3x minus 6 equals 18. Then, we added 6 to both sides, resulting in 3x equals 24. After that, we divided both sides by 3 to find x equals 8. Finally, we verified our solution by substituting x equals 8 back into the original equation. Therefore, the solution to the equation is x equals 8.